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Groups > sci.math > #630960 > unrolled thread
| Started by | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| First post | 2024-09-02 19:07 +0200 |
| Last post | 2024-10-27 17:12 +0100 |
| Articles |
20 on this page of 1000+
— 13 participants
Thread has 2234 articles; only the first 1000 are indexed. |
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Thread has 2234 articles; showing the first 1000 in depth-first order. Use the flat group view to see the rest.
How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-02 19:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-02 13:19 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-02 22:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-02 17:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 12:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-03 07:29 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 13:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-03 23:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-03 00:25 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-03 12:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-03 13:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-04 21:10 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-04 16:52 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-05 13:53 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-05 14:56 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-05 22:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-06 00:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-06 00:45 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-06 00:46 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-06 00:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-06 00:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-06 14:24 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-06 22:01 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-06 14:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-06 12:26 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-06 14:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-06 15:42 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-06 22:42 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-07 11:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 12:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-07 11:56 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-07 13:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-07 13:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 15:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-07 09:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 15:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-07 10:49 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-08 21:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-08 16:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-09 07:32 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 16:53 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:15 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:49 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 21:03 +0200
Re: quantifier order joes <noreply@example.org> - 2024-09-09 19:55 +0000
Re: quantifier order WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 18:24 +0200
Re: quantifier order Richard Damon <richard@damon-family.org> - 2024-09-10 21:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:41 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:41 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 21:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 11:49 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:08 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 16:02 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-09 18:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-09 21:25 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-08 20:25 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-08 22:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-09 07:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 11:46 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 16:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:15 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:49 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 21:05 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-09 16:08 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 02:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 02:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 11:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 11:38 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 21:13 +0200
Re: density of the reals joes <noreply@example.org> - 2024-09-11 06:05 +0000
Re: density of the reals WM <wolfgang.mueckenheim@tha.de> - 2024-09-11 16:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 21:30 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:33 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 22:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:48 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:49 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:56 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-21 17:52 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 21:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-09 06:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 14:04 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-07 08:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 15:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-07 09:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-07 13:37 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-07 15:45 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-07 10:51 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-07 16:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-08 21:52 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-08 16:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:31 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-09 07:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:01 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:14 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:51 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 21:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-10 05:59 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:59 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 21:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-09 15:50 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-09 15:57 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-11-05 15:48 -0800
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 07:52 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 11:51 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 08:03 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-08 20:16 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-09 07:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-07 16:05 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-08 21:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-08 20:06 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:24 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 15:15 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 20:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-09 15:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 18:16 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-10 17:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-11 16:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-11 14:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-11 21:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-09 19:57 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-09 22:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 02:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 18:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 08:07 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 21:10 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 21:58 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-08 22:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 12:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-09 16:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 17:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Python <python@invalid.org> - 2024-09-09 17:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-09 18:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-09 20:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-09 16:02 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-10 07:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 11:42 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 12:05 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 21:31 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:25 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 22:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-10 22:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 16:10 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-10 13:53 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-10 15:18 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-10 20:59 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-10 15:20 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-10 22:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-11 16:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-11 17:29 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-11 21:40 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-11 14:01 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-11 17:13 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-12 11:15 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-12 08:29 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-12 19:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-12 14:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-12 11:37 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-13 17:41 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-13 11:52 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-13 20:05 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-13 16:52 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-13 19:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-14 16:01 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-14 12:33 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-15 21:52 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-15 21:07 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-18 14:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-18 18:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 13:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-19 07:44 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 15:02 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-19 15:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-20 20:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-20 19:02 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 15:41 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-20 16:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 15:47 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-21 13:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 22:11 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-21 18:32 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-22 15:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-22 11:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-22 12:46 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-22 15:20 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-23 07:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-22 14:20 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-19 23:35 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-20 20:13 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-20 17:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-20 19:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 22:02 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-21 19:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-22 15:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-22 14:18 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-22 17:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 12:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 16:28 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-23 01:35 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-23 01:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 18:33 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-22 18:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 11:55 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-22 21:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-22 17:27 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 14:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-22 18:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-19 12:38 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 15:06 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-19 23:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-19 12:11 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-15 14:17 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-15 21:14 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-14 13:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-14 16:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-15 02:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-14 17:18 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-15 04:23 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-14 21:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-21 00:46 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-21 22:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-15 21:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-15 17:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-14 18:35 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-14 17:05 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-15 02:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-14 17:19 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Ben Bacarisse <ben@bsb.me.uk> - 2024-09-15 17:38 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-15 10:06 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Ben Bacarisse <ben@bsb.me.uk> - 2024-09-16 22:47 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-15 12:39 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Ben Bacarisse <ben@bsb.me.uk> - 2024-09-16 23:02 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-16 15:03 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-15 21:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-15 21:09 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-18 14:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-15 21:16 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-16 13:19 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-18 14:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-18 12:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-18 22:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-19 02:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-19 02:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-07 20:37 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 14:55 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-19 12:13 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-19 23:13 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-20 20:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-20 19:06 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 15:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-21 19:25 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-21 16:48 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-22 03:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-21 20:52 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-22 07:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 12:00 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-22 15:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-24 08:00 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-24 12:49 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-24 21:43 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-25 07:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-25 17:23 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-25 16:43 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-25 18:53 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-27 21:08 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-27 19:51 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-29 20:52 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-27 18:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-29 21:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-29 18:29 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-29 17:21 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-09-30 06:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-30 16:59 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-30 17:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-30 19:14 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-01 19:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-02 07:17 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-02 13:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-02 19:03 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-03 20:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-03 18:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 11:23 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-04 06:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-04 15:10 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-04 17:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 20:36 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-04 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-04 14:26 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-04 18:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-04 17:42 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 11:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-09 19:26 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-10 11:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 11:14 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-04 18:45 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 11:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 07:01 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 14:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 09:28 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 20:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-05 14:36 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 22:51 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 13:45 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-06 13:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-07 10:53 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-07 07:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 10:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-08 08:13 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 16:43 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-08 14:01 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-08 12:17 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-09 11:35 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-07 12:56 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 15:42 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-06 13:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-07 10:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-07 11:06 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-07 07:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 10:31 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-08 08:20 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-07 12:57 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-06 11:35 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 15:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-06 13:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-05 14:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 20:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-04 18:46 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 11:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 07:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 12:48 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-04 09:00 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 11:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-04 10:55 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-30 16:59 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-30 07:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-28 07:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-04 12:00 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-25 12:57 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-24 21:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-24 13:19 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-24 20:51 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-25 17:09 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-25 13:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-25 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-25 17:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-25 13:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-25 12:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-25 21:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-25 12:57 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-25 13:44 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-20 16:23 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-21 03:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-20 18:36 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-19 23:39 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-20 20:09 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-20 12:13 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-20 15:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-20 19:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-19 02:31 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-18 18:44 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-19 14:27 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-20 01:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-09 20:11 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-15 21:47 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-16 13:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-16 13:15 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-16 17:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-16 14:56 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-18 11:13 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-10-18 16:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-18 16:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-18 14:01 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-18 17:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-18 14:22 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-18 14:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-18 10:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 12:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-19 12:36 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-19 15:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-19 14:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-20 20:24 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-20 15:51 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-21 22:01 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-22 13:44 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-22 20:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 11:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-22 21:06 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-22 12:09 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 12:16 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-22 13:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 14:12 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-22 19:47 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-22 20:26 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-23 13:53 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-23 14:46 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-23 20:25 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-23 20:28 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-09-23 20:37 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-23 20:55 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-22 16:22 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-23 14:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-23 13:58 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-24 21:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-24 16:19 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-24 22:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-25 00:59 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-25 17:51 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-25 16:39 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-27 20:42 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-09-27 20:12 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-27 22:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-27 22:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-29 20:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-30 07:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-27 21:20 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-09-28 22:11 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-28 07:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-25 14:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-27 20:54 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-28 07:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-29 21:08 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-09-29 13:53 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-09-30 07:10 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-29 15:56 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-30 17:12 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-30 14:33 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-09-30 20:54 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-09-30 15:51 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-01 19:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Jim Burns <james.g.burns@att.net> - 2024-10-01 16:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-02 13:10 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-02 07:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-02 13:54 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-02 15:44 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-03 20:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-03 14:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-03 21:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-03 17:00 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-03 21:18 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-04 08:17 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-04 10:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 11:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-04 06:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 12:11 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? FromTheRafters <FTR@nomail.afraid.org> - 2024-10-04 06:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-04 20:25 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? joes <noreply@example.org> - 2024-10-05 08:10 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 10:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 11:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 07:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 14:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 09:32 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 21:04 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 22:57 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 13:46 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-06 13:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-05 14:44 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 12:58 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Richard Damon <richard@damon-family.org> - 2024-10-05 09:35 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 13:57 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 16:55 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 16:05 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-05 09:21 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 18:54 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 17:08 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 19:09 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-05 14:48 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 19:13 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 16:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 16:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 19:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 19:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 20:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Moebius <invalid@example.invalid> - 2024-10-05 21:02 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? WM <wolfgang.mueckenheim@tha.de> - 2024-10-05 21:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? Alan Mackenzie <acm@muc.de> - 2024-10-05 21:57 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-05 17:37 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-05 20:23 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-06 10:16 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 15:52 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-06 14:52 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-06 17:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-06 15:48 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-06 18:14 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-07 10:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-07 07:14 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-07 09:41 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-07 08:05 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-07 11:08 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-07 15:18 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 12:51 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-08 13:24 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 17:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-08 14:01 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-09 11:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-09 08:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-08 19:27 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-08 16:33 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-08 11:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-07 13:19 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-07 12:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-07 16:11 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-07 13:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-07 13:29 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-07 16:44 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-08 12:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-08 06:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-08 08:29 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-08 12:51 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-08 17:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-08 14:40 -0700
Re: Cardinality joes <noreply@example.org> - 2024-10-08 13:39 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-08 12:45 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-08 21:08 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-09 14:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-09 14:13 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-09 16:40 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-09 15:11 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-09 17:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-09 12:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-09 18:41 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-09 13:57 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-09 14:07 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-10 20:25 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-10 15:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-10 13:42 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-10 23:41 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-10 23:47 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-11 00:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-10 20:22 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-09 16:12 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-09 18:47 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-09 19:13 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-10 20:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-10 18:45 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-10 20:53 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-10 19:54 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 19:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Tom Bola <Tom@bolamail.etc> - 2024-10-12 20:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:55 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-12 19:23 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 21:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-12 22:50 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Tom Bola <Tom@bolamail.etc> - 2024-10-12 22:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-12 13:36 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-14 07:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 12:02 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 15:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 16:01 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-14 15:22 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 12:15 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 15:40 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 16:04 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-14 18:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-14 18:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 19:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 22:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-21 14:05 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 18:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-14 15:27 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:30 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-16 05:19 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 17:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-16 12:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 18:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 11:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-16 15:48 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-17 20:14 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-17 15:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-18 08:05 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-16 15:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 20:18 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 11:02 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 20:18 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-17 20:46 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-17 15:23 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-17 21:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 10:23 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-19 07:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-20 23:04 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 09:14 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-21 00:37 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 10:02 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 22:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-21 08:17 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 10:59 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-15 15:51 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-15 11:29 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-15 13:22 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 10:55 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 11:06 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 11:08 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 11:09 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-16 18:05 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-17 07:25 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-17 11:20 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-17 15:39 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-17 21:56 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-18 05:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-18 13:50 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-18 17:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-18 18:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 09:59 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-19 22:48 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-18 08:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 10:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 06:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 13:00 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 07:07 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-19 06:56 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 13:10 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 07:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 13:53 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 10:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 18:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-19 14:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 20:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-19 18:08 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 09:40 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 07:20 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 07:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 10:17 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 11:58 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 16:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-20 14:50 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 21:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 16:42 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-22 20:56 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-20 23:06 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 01:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 01:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 19:02 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 07:11 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-19 22:48 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 09:51 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 07:13 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 07:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-20 22:43 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 01:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 09:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-17 13:21 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-17 22:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-17 16:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:45 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:17 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 10:55 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-16 15:52 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 13:21 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 13:25 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-16 13:28 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:45 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-12 22:50 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 13:35 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 11:57 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-10 21:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-10 19:51 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:31 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 12:17 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:45 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 09:23 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-10 21:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-10 21:11 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-10 21:12 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-10 21:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-10 20:19 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-11 05:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-11 12:29 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-11 07:06 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-11 14:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-11 13:48 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-12 20:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-11 18:12 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:35 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 12:00 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 15:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 15:53 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 18:29 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:33 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:41 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-13 11:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-11 12:29 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-11 18:15 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-11 20:51 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-13 11:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:25 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-10 19:48 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 15:32 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 10:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-12 16:07 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-14 07:14 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-15 22:40 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:21 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-14 12:04 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-14 15:24 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 12:20 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-12 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-12 17:10 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:59 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-09 18:56 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-09 17:47 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-10 20:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-09 17:40 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-10 20:12 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-12 22:44 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-13 10:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 15:13 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-10 16:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-10 17:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-11 00:22 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-11 09:48 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-11 14:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-12 20:06 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-13 12:28 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 16:43 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-14 13:13 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 20:07 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-14 15:47 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-14 22:03 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-14 20:00 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 10:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 07:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 19:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-16 20:18 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-17 20:46 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-17 13:17 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-17 21:26 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 11:24 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-19 11:21 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-19 14:06 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 15:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-19 15:27 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 20:09 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 10:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-19 22:48 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 09:54 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 07:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 21:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 15:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 21:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 17:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-16 11:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-16 18:55 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-16 17:26 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-16 18:39 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-17 20:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-17 18:39 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-17 20:44 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-17 20:52 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-17 21:22 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-17 23:30 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 10:10 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-19 01:20 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-19 14:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-19 12:20 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 15:38 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-19 14:24 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 19:06 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-19 17:32 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 19:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-19 18:22 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 21:02 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-19 20:19 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 09:30 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-20 09:39 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 11:59 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-20 12:56 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 16:27 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 10:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 15:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 16:28 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 15:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 21:39 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 12:57 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 12:57 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 01:37 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 19:08 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-21 22:18 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 17:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 17:57 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 15:16 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 15:30 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 18:19 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-19 22:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-19 22:48 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 12:00 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-19 14:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 20:22 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-19 15:21 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 20:04 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-20 23:02 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-17 15:41 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-17 18:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 10:16 +0200
Re: Even numbers joes <noreply@example.org> - 2024-10-19 11:31 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-19 12:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 11:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 12:40 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 13:43 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-19 20:19 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-19 18:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-19 18:56 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-20 09:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-20 09:30 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-20 14:33 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-20 17:20 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-21 12:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-21 11:09 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-22 17:49 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-23 11:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-23 10:38 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-25 15:44 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-26 09:22 -0700
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-28 16:15 -0400
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-28 14:45 -0700
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-29 10:38 -0400
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-29 22:27 -0700
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-30 12:18 -0400
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-30 11:34 -0700
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-30 14:55 -0400
Re: How many different unit f [actions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-30 13:00 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 09:48 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-20 09:21 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 11:49 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Alan Mackenzie <acm@muc.de> - 2024-10-20 12:20 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 07:56 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 16:26 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-20 10:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 11:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 15:31 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-20 21:50 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-20 12:53 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-20 17:54 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 10:09 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-21 01:55 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-21 05:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 12:01 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-21 07:10 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-21 08:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-21 20:25 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-21 16:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-21 14:16 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-22 10:13 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-22 10:37 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-22 12:03 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-22 18:12 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-22 13:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-22 20:34 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-23 14:39 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-24 12:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-24 13:34 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-24 10:58 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-10-25 10:49 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-24 20:58 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-24 12:46 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-24 21:51 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-25 00:33 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-25 13:42 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-25 10:53 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-25 18:57 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-25 11:50 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-25 15:05 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-25 21:15 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Jim Burns <james.g.burns@att.net> - 2024-10-25 23:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-26 18:04 +0200
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-26 12:35 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-27 08:38 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-27 07:38 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-27 09:39 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-27 17:15 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-27 18:09 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-27 15:01 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-28 10:49 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-28 07:17 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-28 20:42 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-28 14:06 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-28 23:28 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-28 19:58 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-29 09:36 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-29 07:09 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-29 11:55 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-29 15:16 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-28 10:07 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-28 21:05 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-28 16:51 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-29 09:26 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-29 06:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-30 12:53 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-30 08:57 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-30 15:04 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-30 11:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-30 20:48 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-30 13:04 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-30 13:05 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-30 21:17 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-30 21:19 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-30 13:33 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-30 13:34 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-30 22:14 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-30 22:53 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 09:27 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-30 16:24 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 09:24 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-31 04:29 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 09:41 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-31 05:04 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 10:31 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-31 07:00 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 16:38 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-31 12:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 18:24 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 19:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-31 12:27 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) FromTheRafters <FTR@nomail.afraid.org> - 2024-10-31 15:49 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-31 13:08 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 19:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 07:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 18:33 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 19:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 07:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-31 12:24 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 07:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-31 12:32 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 19:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-30 13:00 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 07:36 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-31 18:28 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-31 20:46 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-31 22:36 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-01 11:07 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-01 20:55 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-02 11:23 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-02 12:02 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-02 18:56 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-02 16:30 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-02 22:37 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-02 20:17 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-11-02 20:38 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-03 12:42 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-03 07:13 -0500
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-03 15:09 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-03 16:21 -0500
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-04 12:04 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-04 07:12 -0500
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-04 18:10 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-11-04 22:08 -0500
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-11-03 14:53 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-03 17:55 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-11-02 12:30 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-11-02 13:36 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-11-02 13:42 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-11-02 14:03 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-02 18:40 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-11-02 18:36 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-31 19:43 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-28 20:21 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-27 17:20 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-27 14:00 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-28 11:42 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Richard Damon <richard@damon-family.org> - 2024-10-28 07:17 -0400
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-28 12:35 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) joes <noreply@example.org> - 2024-10-28 16:33 +0000
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <wolfgang.mueckenheim@tha.de> - 2024-10-28 21:07 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-10-27 12:54 -0700
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) Moebius <invalid@example.invalid> - 2024-10-27 14:54 +0100
Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary) WM <invalid@no.org> - 2024-10-27 17:12 +0100
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-22 12:16 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vcpqdo$2aavq$8@dont-email.me> |
| In reply to | #631586 |
On 9/22/2024 12:09 PM, Ross Finlayson wrote: > On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >> On 9/22/2024 11:37 AM, WM wrote: >>> On 22.09.2024 19:44, Jim Burns wrote: >>> >>>> There is no point next to 0. >>>> >>> This is definite: There is a smallest unit fraction because there are >>> no unit fractions without a first one when counting from zero. >> >> Huh? Wow... Hummm... You suffer from some sort of learning disorder? Or, >> pure troll? Humm... >> >> There is no smallest unit fraction. > > In iota-values there is. The _smallest_ unit fraction, as in they are not infinite? Humm... Keep in mind that if you give me a unit fraction, I can always find a smaller one... > > That's what iota-values are, beyond the "infinite-divisible", > the "infinitely-divided", _together_, as with regards to > "asymptotic equipartitioning" and "uniformization in the limit", > why it is so that what we were told in pre-calculus class, > that 1/oo was not a thing, for the standard linear curriculum, > has that it is a thing, and that this includes things like > "I can interpret .999... as either ~1.0... or .997, .998, ...", > with of course knowing when and where it's either way. > > Also this is one of Aristotle's notions, where Aristotle > also more than 2000 years ago, describes "I can interpret .999..." > about knowing which way is up. > > So, here sometimes it's called "Aristotle's continuum" as with > regards to that otherwise of course the complete ordered field > as Archimedes' and Eudoxus' continuum, later though Whig-ed out > as it were with continental flavour, or Cauchy-Weierstrass, who > give what's called "standard real analysis" these days. > > The idea of "iota" values as "standard infinitesimals" > makes about most sense as that's what "iota" means, the word. > >
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2024-09-22 13:54 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <zj-dnW22ieu1GW37nZ2dnZfqnPqdnZ2d@giganews.com> |
| In reply to | #631587 |
On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: > On 9/22/2024 12:09 PM, Ross Finlayson wrote: >> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>> On 9/22/2024 11:37 AM, WM wrote: >>>> On 22.09.2024 19:44, Jim Burns wrote: >>>> >>>>> There is no point next to 0. >>>>> >>>> This is definite: There is a smallest unit fraction because there are >>>> no unit fractions without a first one when counting from zero. >>> >>> Huh? Wow... Hummm... You suffer from some sort of learning disorder? Or, >>> pure troll? Humm... >>> >>> There is no smallest unit fraction. >> >> In iota-values there is. > > The _smallest_ unit fraction, as in they are not infinite? Humm... Keep > in mind that if you give me a unit fraction, I can always find a smaller > one... > > >> >> That's what iota-values are, beyond the "infinite-divisible", >> the "infinitely-divided", _together_, as with regards to >> "asymptotic equipartitioning" and "uniformization in the limit", >> why it is so that what we were told in pre-calculus class, >> that 1/oo was not a thing, for the standard linear curriculum, >> has that it is a thing, and that this includes things like >> "I can interpret .999... as either ~1.0... or .997, .998, ...", >> with of course knowing when and where it's either way. >> >> Also this is one of Aristotle's notions, where Aristotle >> also more than 2000 years ago, describes "I can interpret .999..." >> about knowing which way is up. >> >> So, here sometimes it's called "Aristotle's continuum" as with >> regards to that otherwise of course the complete ordered field >> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >> as it were with continental flavour, or Cauchy-Weierstrass, who >> give what's called "standard real analysis" these days. >> >> The idea of "iota" values as "standard infinitesimals" >> makes about most sense as that's what "iota" means, the word. >> >> > Nope, in iota-values, they're already smallest. If you look into "asymptotic equipartitioning" and for example "Jordan measure", in the "asymptotic equipartitioning" you can often find another "a.e.: almost everywhere", which is what happens when set theory results not being able to agree with itself, that purposefully and axiomatically it's stipulated to erase the difference, from "everywhere", which some see as an acceptable conceit, others as hypocritical, same thing. In field-reals of course there's that division is _closed_ the operator, except of course usually division-by-zero, where of course delta-epsilonics builds a case for induction that "in the infinite limit" then that it goes to zero, "infinitesimal", in all the powers of division of integers. These though are "line-reals", another own "continuous domain", and constructively, also.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-22 14:12 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vcq189$2bq05$1@dont-email.me> |
| In reply to | #631591 |
On 9/22/2024 1:54 PM, Ross Finlayson wrote: > On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>> On 9/22/2024 11:37 AM, WM wrote: >>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>> >>>>>> There is no point next to 0. >>>>>> >>>>> This is definite: There is a smallest unit fraction because there are >>>>> no unit fractions without a first one when counting from zero. >>>> >>>> Huh? Wow... Hummm... You suffer from some sort of learning disorder? >>>> Or, >>>> pure troll? Humm... >>>> >>>> There is no smallest unit fraction. >>> >>> In iota-values there is. >> >> The _smallest_ unit fraction, as in they are not infinite? Humm... Keep >> in mind that if you give me a unit fraction, I can always find a smaller >> one... >> >> >>> >>> That's what iota-values are, beyond the "infinite-divisible", >>> the "infinitely-divided", _together_, as with regards to >>> "asymptotic equipartitioning" and "uniformization in the limit", >>> why it is so that what we were told in pre-calculus class, >>> that 1/oo was not a thing, for the standard linear curriculum, >>> has that it is a thing, and that this includes things like >>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>> with of course knowing when and where it's either way. >>> >>> Also this is one of Aristotle's notions, where Aristotle >>> also more than 2000 years ago, describes "I can interpret .999..." >>> about knowing which way is up. >>> >>> So, here sometimes it's called "Aristotle's continuum" as with >>> regards to that otherwise of course the complete ordered field >>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>> as it were with continental flavour, or Cauchy-Weierstrass, who >>> give what's called "standard real analysis" these days. >>> >>> The idea of "iota" values as "standard infinitesimals" >>> makes about most sense as that's what "iota" means, the word. >>> >>> >> > > Nope, in iota-values, they're already smallest. What about an individual smallest unit fraction? You can say they get arbitrarily close to zero, but that still does not mean there is a smallest one... > > If you look into "asymptotic equipartitioning" and > for example "Jordan measure", in the "asymptotic equipartitioning" > you can often find another "a.e.: almost everywhere", > which is what happens when set theory results not being > able to agree with itself, that purposefully and axiomatically > it's stipulated to erase the difference, from "everywhere", > which some see as an acceptable conceit, others as hypocritical, > same thing. > > In field-reals of course there's that division is _closed_ > the operator, except of course usually division-by-zero, > where of course delta-epsilonics builds a case for induction > that "in the infinite limit" then that it goes to zero, > "infinitesimal", in all the powers of division of integers. > > These though are "line-reals", another own "continuous domain", > and constructively, also. > >
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2024-09-22 19:47 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <v66dnVZHn9pAS237nZ2dnZfqnPSdnZ2d@giganews.com> |
| In reply to | #631592 |
On 09/22/2024 02:12 PM, Chris M. Thomasson wrote: > On 9/22/2024 1:54 PM, Ross Finlayson wrote: >> On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >>> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>>> On 9/22/2024 11:37 AM, WM wrote: >>>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>>> >>>>>>> There is no point next to 0. >>>>>>> >>>>>> This is definite: There is a smallest unit fraction because there are >>>>>> no unit fractions without a first one when counting from zero. >>>>> >>>>> Huh? Wow... Hummm... You suffer from some sort of learning >>>>> disorder? Or, >>>>> pure troll? Humm... >>>>> >>>>> There is no smallest unit fraction. >>>> >>>> In iota-values there is. >>> >>> The _smallest_ unit fraction, as in they are not infinite? Humm... Keep >>> in mind that if you give me a unit fraction, I can always find a smaller >>> one... >>> >>> >>>> >>>> That's what iota-values are, beyond the "infinite-divisible", >>>> the "infinitely-divided", _together_, as with regards to >>>> "asymptotic equipartitioning" and "uniformization in the limit", >>>> why it is so that what we were told in pre-calculus class, >>>> that 1/oo was not a thing, for the standard linear curriculum, >>>> has that it is a thing, and that this includes things like >>>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>>> with of course knowing when and where it's either way. >>>> >>>> Also this is one of Aristotle's notions, where Aristotle >>>> also more than 2000 years ago, describes "I can interpret .999..." >>>> about knowing which way is up. >>>> >>>> So, here sometimes it's called "Aristotle's continuum" as with >>>> regards to that otherwise of course the complete ordered field >>>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>>> as it were with continental flavour, or Cauchy-Weierstrass, who >>>> give what's called "standard real analysis" these days. >>>> >>>> The idea of "iota" values as "standard infinitesimals" >>>> makes about most sense as that's what "iota" means, the word. >>>> >>>> >>> >> >> Nope, in iota-values, they're already smallest. > > What about an individual smallest unit fraction? You can say they get > arbitrarily close to zero, but that still does not mean there is a > smallest one... > >> >> If you look into "asymptotic equipartitioning" and >> for example "Jordan measure", in the "asymptotic equipartitioning" >> you can often find another "a.e.: almost everywhere", >> which is what happens when set theory results not being >> able to agree with itself, that purposefully and axiomatically >> it's stipulated to erase the difference, from "everywhere", >> which some see as an acceptable conceit, others as hypocritical, >> same thing. >> >> In field-reals of course there's that division is _closed_ >> the operator, except of course usually division-by-zero, >> where of course delta-epsilonics builds a case for induction >> that "in the infinite limit" then that it goes to zero, >> "infinitesimal", in all the powers of division of integers. >> >> These though are "line-reals", another own "continuous domain", >> and constructively, also. >> >> > In field-reals there's no smallest magnitude non-zero, in line-reals there's a smallest magnitude non-zero. Each of field-reals and line-reals model a continuous domain, with the usual R, field-reals and then "a unit length interval, contiguous, defined for example as f(n) = n/d as 0 <= n <= d, d -> oo", then that a usual representation of any real magnitude or signed-magnitude is integer-part and non-integer part, the [0,1] being the non-integer part, and a dual representation bit for example just like field-reals have dual representation .999... = 1. Then, they don't go together and aren't added to together, field-reals and line-reals, except with regards to the book-keeping involved their values as magnitudes, and properties of those according to other matters of relation. I.e., they're not interchangeable, as they're not same, and have different definitions of continuity, yet in set theory they're each sets, then it results that just like there's a result in usual set theory that sets with different cardinals have no function between them, here it's that these are defined about their bounds and result being a "non-Cartesian", function in set theory what defines them, so, it's just another profound result in all of set theory. You might even figure it'll make the news someday. Here though it's old news. "real-valued"
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-22 20:26 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vcqn5l$2id8a$1@dont-email.me> |
| In reply to | #631603 |
On 9/22/2024 7:47 PM, Ross Finlayson wrote: > On 09/22/2024 02:12 PM, Chris M. Thomasson wrote: >> On 9/22/2024 1:54 PM, Ross Finlayson wrote: >>> On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >>>> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>>>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>>>> On 9/22/2024 11:37 AM, WM wrote: >>>>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>>>> >>>>>>>> There is no point next to 0. >>>>>>>> >>>>>>> This is definite: There is a smallest unit fraction because there >>>>>>> are >>>>>>> no unit fractions without a first one when counting from zero. >>>>>> >>>>>> Huh? Wow... Hummm... You suffer from some sort of learning >>>>>> disorder? Or, >>>>>> pure troll? Humm... >>>>>> >>>>>> There is no smallest unit fraction. >>>>> >>>>> In iota-values there is. >>>> >>>> The _smallest_ unit fraction, as in they are not infinite? Humm... Keep >>>> in mind that if you give me a unit fraction, I can always find a >>>> smaller >>>> one... >>>> >>>> >>>>> >>>>> That's what iota-values are, beyond the "infinite-divisible", >>>>> the "infinitely-divided", _together_, as with regards to >>>>> "asymptotic equipartitioning" and "uniformization in the limit", >>>>> why it is so that what we were told in pre-calculus class, >>>>> that 1/oo was not a thing, for the standard linear curriculum, >>>>> has that it is a thing, and that this includes things like >>>>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>>>> with of course knowing when and where it's either way. >>>>> >>>>> Also this is one of Aristotle's notions, where Aristotle >>>>> also more than 2000 years ago, describes "I can interpret .999..." >>>>> about knowing which way is up. >>>>> >>>>> So, here sometimes it's called "Aristotle's continuum" as with >>>>> regards to that otherwise of course the complete ordered field >>>>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>>>> as it were with continental flavour, or Cauchy-Weierstrass, who >>>>> give what's called "standard real analysis" these days. >>>>> >>>>> The idea of "iota" values as "standard infinitesimals" >>>>> makes about most sense as that's what "iota" means, the word. >>>>> >>>>> >>>> >>> >>> Nope, in iota-values, they're already smallest. >> >> What about an individual smallest unit fraction? You can say they get >> arbitrarily close to zero, but that still does not mean there is a >> smallest one... >> >>> >>> If you look into "asymptotic equipartitioning" and >>> for example "Jordan measure", in the "asymptotic equipartitioning" >>> you can often find another "a.e.: almost everywhere", >>> which is what happens when set theory results not being >>> able to agree with itself, that purposefully and axiomatically >>> it's stipulated to erase the difference, from "everywhere", >>> which some see as an acceptable conceit, others as hypocritical, >>> same thing. >>> >>> In field-reals of course there's that division is _closed_ >>> the operator, except of course usually division-by-zero, >>> where of course delta-epsilonics builds a case for induction >>> that "in the infinite limit" then that it goes to zero, >>> "infinitesimal", in all the powers of division of integers. >>> >>> These though are "line-reals", another own "continuous domain", >>> and constructively, also. >>> >>> >> > > In field-reals there's no smallest magnitude non-zero, > in line-reals there's a smallest magnitude non-zero. > > Each of field-reals and line-reals model a continuous > domain, with the usual R, field-reals and then > "a unit length interval, contiguous, defined for > example as f(n) = n/d as 0 <= n <= d, d -> oo", > then that a usual representation of any real > magnitude or signed-magnitude is integer-part > and non-integer part, the [0,1] being the non-integer > part, and a dual representation bit for example just > like field-reals have dual representation .999... = 1. > > Then, they don't go together and aren't added to together, > field-reals and line-reals, except with regards to the > book-keeping involved their values as magnitudes, and > properties of those according to other matters of relation. > > I.e., they're not interchangeable, as they're not same, > and have different definitions of continuity, yet in set > theory they're each sets, then it results that just like > there's a result in usual set theory that sets with > different cardinals have no function between them, > here it's that these are defined about their bounds > and result being a "non-Cartesian", function in set > theory what defines them, so, it's just another > profound result in all of set theory. > > You might even figure it'll make the news someday. > > Here though it's old news. How does it define the smallest possible unit fraction? 1/n ? It cannot be an actual example unit fraction because there will always be another one that is smaller...
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2024-09-23 13:53 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <6lKdnaipCOmlSGz7nZ2dnZfqn_qdnZ2d@giganews.com> |
| In reply to | #631604 |
On 09/22/2024 08:26 PM, Chris M. Thomasson wrote: > On 9/22/2024 7:47 PM, Ross Finlayson wrote: >> On 09/22/2024 02:12 PM, Chris M. Thomasson wrote: >>> On 9/22/2024 1:54 PM, Ross Finlayson wrote: >>>> On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >>>>> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>>>>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>>>>> On 9/22/2024 11:37 AM, WM wrote: >>>>>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>>>>> >>>>>>>>> There is no point next to 0. >>>>>>>>> >>>>>>>> This is definite: There is a smallest unit fraction because >>>>>>>> there are >>>>>>>> no unit fractions without a first one when counting from zero. >>>>>>> >>>>>>> Huh? Wow... Hummm... You suffer from some sort of learning >>>>>>> disorder? Or, >>>>>>> pure troll? Humm... >>>>>>> >>>>>>> There is no smallest unit fraction. >>>>>> >>>>>> In iota-values there is. >>>>> >>>>> The _smallest_ unit fraction, as in they are not infinite? Humm... >>>>> Keep >>>>> in mind that if you give me a unit fraction, I can always find a >>>>> smaller >>>>> one... >>>>> >>>>> >>>>>> >>>>>> That's what iota-values are, beyond the "infinite-divisible", >>>>>> the "infinitely-divided", _together_, as with regards to >>>>>> "asymptotic equipartitioning" and "uniformization in the limit", >>>>>> why it is so that what we were told in pre-calculus class, >>>>>> that 1/oo was not a thing, for the standard linear curriculum, >>>>>> has that it is a thing, and that this includes things like >>>>>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>>>>> with of course knowing when and where it's either way. >>>>>> >>>>>> Also this is one of Aristotle's notions, where Aristotle >>>>>> also more than 2000 years ago, describes "I can interpret .999..." >>>>>> about knowing which way is up. >>>>>> >>>>>> So, here sometimes it's called "Aristotle's continuum" as with >>>>>> regards to that otherwise of course the complete ordered field >>>>>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>>>>> as it were with continental flavour, or Cauchy-Weierstrass, who >>>>>> give what's called "standard real analysis" these days. >>>>>> >>>>>> The idea of "iota" values as "standard infinitesimals" >>>>>> makes about most sense as that's what "iota" means, the word. >>>>>> >>>>>> >>>>> >>>> >>>> Nope, in iota-values, they're already smallest. >>> >>> What about an individual smallest unit fraction? You can say they get >>> arbitrarily close to zero, but that still does not mean there is a >>> smallest one... >>> >>>> >>>> If you look into "asymptotic equipartitioning" and >>>> for example "Jordan measure", in the "asymptotic equipartitioning" >>>> you can often find another "a.e.: almost everywhere", >>>> which is what happens when set theory results not being >>>> able to agree with itself, that purposefully and axiomatically >>>> it's stipulated to erase the difference, from "everywhere", >>>> which some see as an acceptable conceit, others as hypocritical, >>>> same thing. >>>> >>>> In field-reals of course there's that division is _closed_ >>>> the operator, except of course usually division-by-zero, >>>> where of course delta-epsilonics builds a case for induction >>>> that "in the infinite limit" then that it goes to zero, >>>> "infinitesimal", in all the powers of division of integers. >>>> >>>> These though are "line-reals", another own "continuous domain", >>>> and constructively, also. >>>> >>>> >>> >> >> In field-reals there's no smallest magnitude non-zero, >> in line-reals there's a smallest magnitude non-zero. >> >> Each of field-reals and line-reals model a continuous >> domain, with the usual R, field-reals and then >> "a unit length interval, contiguous, defined for >> example as f(n) = n/d as 0 <= n <= d, d -> oo", >> then that a usual representation of any real >> magnitude or signed-magnitude is integer-part >> and non-integer part, the [0,1] being the non-integer >> part, and a dual representation bit for example just >> like field-reals have dual representation .999... = 1. >> >> Then, they don't go together and aren't added to together, >> field-reals and line-reals, except with regards to the >> book-keeping involved their values as magnitudes, and >> properties of those according to other matters of relation. >> >> I.e., they're not interchangeable, as they're not same, >> and have different definitions of continuity, yet in set >> theory they're each sets, then it results that just like >> there's a result in usual set theory that sets with >> different cardinals have no function between them, >> here it's that these are defined about their bounds >> and result being a "non-Cartesian", function in set >> theory what defines them, so, it's just another >> profound result in all of set theory. >> >> You might even figure it'll make the news someday. >> >> Here though it's old news. > > How does it define the smallest possible unit fraction? 1/n ? It cannot > be an actual example unit fraction because there will always be another > one that is smaller... > Nope, it's defined for natural integers f(n) and there are no integers strictly between 0 and 1. It's the properties of the entire range of this function what make it's fixed, scalarly, matters of perspective, and as with regards to that it's built before even considerations of otherwise fractions even exist. Then, so defined as the range of a function, it's not a usual function, as it simply can't be re-ordered, as that's not how it's defined. It's defined of very primitive elements and very simple aspects of laws of arithmetic, then with a usual apparatus of the infinite limit, et voila: iota-values, real-valued, according to laws of arithmetic. It's not the field-reals, it's the line-reals, and it's shewn that as either is a continuous domain, either is a model of the Linear Continuum. Then that one needs infinite limit and, the other needs not, yet the one without then must axiomatize itself its own completion according to Pythagoreans, lines-reals and field-reals, have here that Aristotle helps establish that since antiquity there are both considerations.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-23 14:46 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vcsnj6$2s1qd$4@dont-email.me> |
| In reply to | #631615 |
On 9/23/2024 1:53 PM, Ross Finlayson wrote: > On 09/22/2024 08:26 PM, Chris M. Thomasson wrote: >> On 9/22/2024 7:47 PM, Ross Finlayson wrote: >>> On 09/22/2024 02:12 PM, Chris M. Thomasson wrote: >>>> On 9/22/2024 1:54 PM, Ross Finlayson wrote: >>>>> On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >>>>>> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>>>>>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>>>>>> On 9/22/2024 11:37 AM, WM wrote: >>>>>>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>>>>>> >>>>>>>>>> There is no point next to 0. >>>>>>>>>> >>>>>>>>> This is definite: There is a smallest unit fraction because >>>>>>>>> there are >>>>>>>>> no unit fractions without a first one when counting from zero. >>>>>>>> >>>>>>>> Huh? Wow... Hummm... You suffer from some sort of learning >>>>>>>> disorder? Or, >>>>>>>> pure troll? Humm... >>>>>>>> >>>>>>>> There is no smallest unit fraction. >>>>>>> >>>>>>> In iota-values there is. >>>>>> >>>>>> The _smallest_ unit fraction, as in they are not infinite? Humm... >>>>>> Keep >>>>>> in mind that if you give me a unit fraction, I can always find a >>>>>> smaller >>>>>> one... >>>>>> >>>>>> >>>>>>> >>>>>>> That's what iota-values are, beyond the "infinite-divisible", >>>>>>> the "infinitely-divided", _together_, as with regards to >>>>>>> "asymptotic equipartitioning" and "uniformization in the limit", >>>>>>> why it is so that what we were told in pre-calculus class, >>>>>>> that 1/oo was not a thing, for the standard linear curriculum, >>>>>>> has that it is a thing, and that this includes things like >>>>>>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>>>>>> with of course knowing when and where it's either way. >>>>>>> >>>>>>> Also this is one of Aristotle's notions, where Aristotle >>>>>>> also more than 2000 years ago, describes "I can interpret .999..." >>>>>>> about knowing which way is up. >>>>>>> >>>>>>> So, here sometimes it's called "Aristotle's continuum" as with >>>>>>> regards to that otherwise of course the complete ordered field >>>>>>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>>>>>> as it were with continental flavour, or Cauchy-Weierstrass, who >>>>>>> give what's called "standard real analysis" these days. >>>>>>> >>>>>>> The idea of "iota" values as "standard infinitesimals" >>>>>>> makes about most sense as that's what "iota" means, the word. >>>>>>> >>>>>>> >>>>>> >>>>> >>>>> Nope, in iota-values, they're already smallest. >>>> >>>> What about an individual smallest unit fraction? You can say they get >>>> arbitrarily close to zero, but that still does not mean there is a >>>> smallest one... >>>> >>>>> >>>>> If you look into "asymptotic equipartitioning" and >>>>> for example "Jordan measure", in the "asymptotic equipartitioning" >>>>> you can often find another "a.e.: almost everywhere", >>>>> which is what happens when set theory results not being >>>>> able to agree with itself, that purposefully and axiomatically >>>>> it's stipulated to erase the difference, from "everywhere", >>>>> which some see as an acceptable conceit, others as hypocritical, >>>>> same thing. >>>>> >>>>> In field-reals of course there's that division is _closed_ >>>>> the operator, except of course usually division-by-zero, >>>>> where of course delta-epsilonics builds a case for induction >>>>> that "in the infinite limit" then that it goes to zero, >>>>> "infinitesimal", in all the powers of division of integers. >>>>> >>>>> These though are "line-reals", another own "continuous domain", >>>>> and constructively, also. >>>>> >>>>> >>>> >>> >>> In field-reals there's no smallest magnitude non-zero, >>> in line-reals there's a smallest magnitude non-zero. >>> >>> Each of field-reals and line-reals model a continuous >>> domain, with the usual R, field-reals and then >>> "a unit length interval, contiguous, defined for >>> example as f(n) = n/d as 0 <= n <= d, d -> oo", >>> then that a usual representation of any real >>> magnitude or signed-magnitude is integer-part >>> and non-integer part, the [0,1] being the non-integer >>> part, and a dual representation bit for example just >>> like field-reals have dual representation .999... = 1. >>> >>> Then, they don't go together and aren't added to together, >>> field-reals and line-reals, except with regards to the >>> book-keeping involved their values as magnitudes, and >>> properties of those according to other matters of relation. >>> >>> I.e., they're not interchangeable, as they're not same, >>> and have different definitions of continuity, yet in set >>> theory they're each sets, then it results that just like >>> there's a result in usual set theory that sets with >>> different cardinals have no function between them, >>> here it's that these are defined about their bounds >>> and result being a "non-Cartesian", function in set >>> theory what defines them, so, it's just another >>> profound result in all of set theory. >>> >>> You might even figure it'll make the news someday. >>> >>> Here though it's old news. >> >> How does it define the smallest possible unit fraction? 1/n ? It cannot >> be an actual example unit fraction because there will always be another >> one that is smaller... >> > > Nope, it's defined for natural integers f(n) and there are > no integers strictly between 0 and 1. Oh. I failed to understand that you were talking about the granularity of integers. No integer between 0 and 1 for sure. > > It's the properties of the entire range of this function > what make it's fixed, scalarly, matters of perspective, > and as with regards to that it's built before even > considerations of otherwise fractions even exist. > > Then, so defined as the range of a function, it's > not a usual function, as it simply can't be re-ordered, > as that's not how it's defined. > > It's defined of very primitive elements and very simple > aspects of laws of arithmetic, then with a usual apparatus > of the infinite limit, et voila: iota-values, real-valued, > according to laws of arithmetic. > > It's not the field-reals, it's the line-reals, and it's > shewn that as either is a continuous domain, either is a > model of the Linear Continuum. > > Then that one needs infinite limit and, the other needs > not, yet the one without then must axiomatize itself > its own completion according to Pythagoreans, lines-reals > and field-reals, have here that Aristotle helps establish > that since antiquity there are both considerations. > >
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2024-09-23 20:25 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <wpGdnUgJebG6rG_7nZ2dnZfqn_WdnZ2d@giganews.com> |
| In reply to | #631616 |
On 09/23/2024 02:46 PM, Chris M. Thomasson wrote: > On 9/23/2024 1:53 PM, Ross Finlayson wrote: >> On 09/22/2024 08:26 PM, Chris M. Thomasson wrote: >>> On 9/22/2024 7:47 PM, Ross Finlayson wrote: >>>> On 09/22/2024 02:12 PM, Chris M. Thomasson wrote: >>>>> On 9/22/2024 1:54 PM, Ross Finlayson wrote: >>>>>> On 09/22/2024 12:16 PM, Chris M. Thomasson wrote: >>>>>>> On 9/22/2024 12:09 PM, Ross Finlayson wrote: >>>>>>>> On 09/22/2024 11:54 AM, Chris M. Thomasson wrote: >>>>>>>>> On 9/22/2024 11:37 AM, WM wrote: >>>>>>>>>> On 22.09.2024 19:44, Jim Burns wrote: >>>>>>>>>> >>>>>>>>>>> There is no point next to 0. >>>>>>>>>>> >>>>>>>>>> This is definite: There is a smallest unit fraction because >>>>>>>>>> there are >>>>>>>>>> no unit fractions without a first one when counting from zero. >>>>>>>>> >>>>>>>>> Huh? Wow... Hummm... You suffer from some sort of learning >>>>>>>>> disorder? Or, >>>>>>>>> pure troll? Humm... >>>>>>>>> >>>>>>>>> There is no smallest unit fraction. >>>>>>>> >>>>>>>> In iota-values there is. >>>>>>> >>>>>>> The _smallest_ unit fraction, as in they are not infinite? Humm... >>>>>>> Keep >>>>>>> in mind that if you give me a unit fraction, I can always find a >>>>>>> smaller >>>>>>> one... >>>>>>> >>>>>>> >>>>>>>> >>>>>>>> That's what iota-values are, beyond the "infinite-divisible", >>>>>>>> the "infinitely-divided", _together_, as with regards to >>>>>>>> "asymptotic equipartitioning" and "uniformization in the limit", >>>>>>>> why it is so that what we were told in pre-calculus class, >>>>>>>> that 1/oo was not a thing, for the standard linear curriculum, >>>>>>>> has that it is a thing, and that this includes things like >>>>>>>> "I can interpret .999... as either ~1.0... or .997, .998, ...", >>>>>>>> with of course knowing when and where it's either way. >>>>>>>> >>>>>>>> Also this is one of Aristotle's notions, where Aristotle >>>>>>>> also more than 2000 years ago, describes "I can interpret .999..." >>>>>>>> about knowing which way is up. >>>>>>>> >>>>>>>> So, here sometimes it's called "Aristotle's continuum" as with >>>>>>>> regards to that otherwise of course the complete ordered field >>>>>>>> as Archimedes' and Eudoxus' continuum, later though Whig-ed out >>>>>>>> as it were with continental flavour, or Cauchy-Weierstrass, who >>>>>>>> give what's called "standard real analysis" these days. >>>>>>>> >>>>>>>> The idea of "iota" values as "standard infinitesimals" >>>>>>>> makes about most sense as that's what "iota" means, the word. >>>>>>>> >>>>>>>> >>>>>>> >>>>>> >>>>>> Nope, in iota-values, they're already smallest. >>>>> >>>>> What about an individual smallest unit fraction? You can say they get >>>>> arbitrarily close to zero, but that still does not mean there is a >>>>> smallest one... >>>>> >>>>>> >>>>>> If you look into "asymptotic equipartitioning" and >>>>>> for example "Jordan measure", in the "asymptotic equipartitioning" >>>>>> you can often find another "a.e.: almost everywhere", >>>>>> which is what happens when set theory results not being >>>>>> able to agree with itself, that purposefully and axiomatically >>>>>> it's stipulated to erase the difference, from "everywhere", >>>>>> which some see as an acceptable conceit, others as hypocritical, >>>>>> same thing. >>>>>> >>>>>> In field-reals of course there's that division is _closed_ >>>>>> the operator, except of course usually division-by-zero, >>>>>> where of course delta-epsilonics builds a case for induction >>>>>> that "in the infinite limit" then that it goes to zero, >>>>>> "infinitesimal", in all the powers of division of integers. >>>>>> >>>>>> These though are "line-reals", another own "continuous domain", >>>>>> and constructively, also. >>>>>> >>>>>> >>>>> >>>> >>>> In field-reals there's no smallest magnitude non-zero, >>>> in line-reals there's a smallest magnitude non-zero. >>>> >>>> Each of field-reals and line-reals model a continuous >>>> domain, with the usual R, field-reals and then >>>> "a unit length interval, contiguous, defined for >>>> example as f(n) = n/d as 0 <= n <= d, d -> oo", >>>> then that a usual representation of any real >>>> magnitude or signed-magnitude is integer-part >>>> and non-integer part, the [0,1] being the non-integer >>>> part, and a dual representation bit for example just >>>> like field-reals have dual representation .999... = 1. >>>> >>>> Then, they don't go together and aren't added to together, >>>> field-reals and line-reals, except with regards to the >>>> book-keeping involved their values as magnitudes, and >>>> properties of those according to other matters of relation. >>>> >>>> I.e., they're not interchangeable, as they're not same, >>>> and have different definitions of continuity, yet in set >>>> theory they're each sets, then it results that just like >>>> there's a result in usual set theory that sets with >>>> different cardinals have no function between them, >>>> here it's that these are defined about their bounds >>>> and result being a "non-Cartesian", function in set >>>> theory what defines them, so, it's just another >>>> profound result in all of set theory. >>>> >>>> You might even figure it'll make the news someday. >>>> >>>> Here though it's old news. >>> >>> How does it define the smallest possible unit fraction? 1/n ? It cannot >>> be an actual example unit fraction because there will always be another >>> one that is smaller... >>> >> >> Nope, it's defined for natural integers f(n) and there are >> no integers strictly between 0 and 1. > > Oh. I failed to understand that you were talking about the granularity > of integers. No integer between 0 and 1 for sure. > >> >> It's the properties of the entire range of this function >> what make it's fixed, scalarly, matters of perspective, >> and as with regards to that it's built before even >> considerations of otherwise fractions even exist. >> >> Then, so defined as the range of a function, it's >> not a usual function, as it simply can't be re-ordered, >> as that's not how it's defined. >> >> It's defined of very primitive elements and very simple >> aspects of laws of arithmetic, then with a usual apparatus >> of the infinite limit, et voila: iota-values, real-valued, >> according to laws of arithmetic. >> >> It's not the field-reals, it's the line-reals, and it's >> shewn that as either is a continuous domain, either is a >> model of the Linear Continuum. >> >> Then that one needs infinite limit and, the other needs >> not, yet the one without then must axiomatize itself >> its own completion according to Pythagoreans, lines-reals >> and field-reals, have here that Aristotle helps establish >> that since antiquity there are both considerations. >> >> > It's part of the whole consterning bit when the notion of something like Zeno's arguments, _start and end at every single point along the way_, of the motion. So, pre-calculus and "since you've been instructed both years of algebra and trigonometry and know your identities and know your manipulations, and of course you know arithmetic, and as well you know geometry, here we're going to introduce delta-epsilonics the brief course of proofs where most everything you learned already was via demonstration or of brief proofs, and made the inductive course after delta-epsilonics given the laws of arithmetic being trichotomy and closure, and establish the definition of the limit and of course what must be the infinite limit", pre-calculus carefully couches this opinion not "the end-all be-all form" of the real numbers, as thusly gently only a matter of delta-epsilonics and that the reals are naively continuous, without necessarily bothering for example with concepts like least-upper-bound or for that matter measure theory, when the fundamental theorem of the derivative is then worked up and then the fundamental theorem of the integral, after trapezoid rule with Riemann sums nice and simple, then it's moreso "we don't thusly need line-reals yet so they're ignored", not "we ignorant and doubly so". Then later such notions as line-reals show up plenty already, for example asymptotic equipartioning, yet here most especially for that ran(EF) makes for that EF is defined on the naturals, yet is integrable and has integral 1, so it's a distribution, also it's a cumulative distribution as it goes to 1, then also there's that it's its own derivative and anti-derivative, so, really, it's nice and special. Aristotle at least was like "you know, if you bother to read more than one paragraph and consider my works as more a thorough summary of the entire library of Alexandria, then maybe you'd know that there being at least two models of continuous domains is at least as old as this". https://antigonejournal.com/2022/06/aristotle-library-alexandria/ McKeon translates a pretty good Aristotle, "constituted out of the definitive Oxford translation", or, it's considered the best edition in English today. https://en.wikipedia.org/wiki/Lyceum_(classical)#Aristotle's_school_and_library So, Zeno's are the classical expositions of these since even further antiquity, and there are supposedly even 20 or 30 more since-lost examples. Anyways it's nice and easy and way down in set theory to get setup that line-reals have for a non-Cartesian function not really saying much or having much said in terms of being contradicted at all. Of course it _must_ be that it falls out of all the arguments for un-countability as un-contradicted, which it does.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-23 20:28 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vctblh$32cko$2@dont-email.me> |
| In reply to | #631620 |
On 9/23/2024 8:25 PM, Ross Finlayson wrote: [...] wrt delta, think of the simple difference between two different points... Once we have the delta its automatically normalized between the two points, say p0 and p1 of a line. So, 0 is p0 and 1 is p1. 0 and 1 are the delta. So .5 would be the mid point. I am missing your main point? Sorry. ;^o
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2024-09-23 20:37 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <jcKdncntWeNirm_7nZ2dnZfqn_SdnZ2d@giganews.com> |
| In reply to | #631621 |
On 09/23/2024 08:28 PM, Chris M. Thomasson wrote: > On 9/23/2024 8:25 PM, Ross Finlayson wrote: > [...] > > wrt delta, think of the simple difference between two different > points... Once we have the delta its automatically normalized between > the two points, say p0 and p1 of a line. So, 0 is p0 and 1 is p1. 0 and > 1 are the delta. So .5 would be the mid point. I am missing your main > point? Sorry. ;^o > Well what you do is you put pencil to paper and draw a line. It doesn't have to be a particularly straight line, yet, just just put pencil to paper and draw a line left-to-right or right-to-left as you will. So, if those are points, you drew them in order. Though, there is an idea called "vague fugue" about that it's always sort of a zig-zag, that's a much, much more abstract notion than that the line, that you drew, marked each point on it: in order. So, they're in a line. Then, if it's an infinitude of them, then all that it is is that the whole thing is. Exactly one of them. "Line-drawing: again in remedial."
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2024-09-23 20:55 -0700 |
| Subject | Re: How many different unit fractions are lessorequal than all unit fractions? (iota-values) |
| Message-ID | <vctd6v$32cko$4@dont-email.me> |
| In reply to | #631622 |
On 9/23/2024 8:37 PM, Ross Finlayson wrote: > On 09/23/2024 08:28 PM, Chris M. Thomasson wrote: >> On 9/23/2024 8:25 PM, Ross Finlayson wrote: >> [...] >> >> wrt delta, think of the simple difference between two different >> points... Once we have the delta its automatically normalized between >> the two points, say p0 and p1 of a line. So, 0 is p0 and 1 is p1. 0 and >> 1 are the delta. So .5 would be the mid point. I am missing your main >> point? Sorry. ;^o >> > > Well what you do is you put pencil to paper and draw a line. Indeed. Agreed. connecting 2-ary point as in indexes into vertices is fun. Think of three points, p0 = 0 p1 = 1/2 p2 = 1 draw_line(p0, p1); draw_line(p1, p2); Okay fine. > > It doesn't have to be a particularly straight line, > yet, just just put pencil to paper and draw a line > left-to-right or right-to-left as you will. > > So, if those are points, you drew them in order. > > > Though, there is an idea called "vague fugue" > about that it's always sort of a zig-zag, > that's a much, much more abstract notion > than that the line, that you drew, marked > each point on it: in order. > > So, they're in a line. > > Then, if it's an infinitude of them, then > all that it is is that the whole thing is. > Exactly one of them. > > "Line-drawing: again in remedial." >
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2024-09-22 16:22 -0400 |
| Message-ID | <6b50a171-8127-4ce6-9bd3-2dc213638e9b@att.net> |
| In reply to | #631579 |
On 9/22/2024 2:37 PM, WM wrote: > On 22.09.2024 19:44, Jim Burns wrote: >> There is no point next to 0. > There is a smallest unit fraction > because > there are no unit fractions without a first one > when counting from zero. [1/2] ∀⅟k ∈ ⅟ℕᵈᵉᶠ: ⅟ℕᵈᵉᶠ ∋ ¼⋅⅟k < ⅟k Each visibleᵂᴹ unit.fraction ⅟k has a counter.example ¼⋅⅟k to its being smallest. [2/2] ¬∃ᴿδ > 0: ¬( δ >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ) No positive point, unit.fraction or otherwise, is NOT undercut by some visible unit fraction. A point undercut by a visibleᵂᴹ unit fraction is not the smallest unit fraction. ⎛ Assume otherwise. ⎜ Assume ⎜ δ > 0 ∧ ¬( δ >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ) ⎜ ⎜ β = glb.⅟ℕᵈᵉᶠ ≥ δ > 0 ⎜ ⎜ ½.β < β ⎜ ¬( ½.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ) ⎜ ⎜ 2.β > β ⎜ 2.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ⎜ ⎜ However, ⎜ 2.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ⎜ 2.β > ⅟k ⎜ ½.β > ¼⋅⅟k ⎜ ½.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ⎜ ⎜ ½.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ∧ ¬( ½.β >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ) ⎝ Contradiction. Therefore, ¬∃ᴿδ > 0: ¬( δ >ₑₓᵢₛₜₛ ⅟ℕᵈᵉᶠ ) Visibleᵂᴹ or darkᵂᴹ, there is no smallest unit fraction.
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2024-09-23 14:57 +0200 |
| Message-ID | <vcroj3$2nfvb$2@dont-email.me> |
| In reply to | #631590 |
On 22.09.2024 22:22, Jim Burns wrote: > On 9/22/2024 2:37 PM, WM wrote: >> On 22.09.2024 19:44, Jim Burns wrote: > >>> There is no point next to 0. > >> There is a smallest unit fraction >> because >> there are no unit fractions without a first one >> when counting from zero. > > Each visibleᵂᴹ unit.fraction ⅟k has > a counter.example ¼⋅⅟k to its being smallest. Yes. Therefore the smallest unit fraction must be dark. > No positive point, unit.fraction or otherwise, > is NOT undercut by some visible unit fraction. Wrong. NUF(x) grows from 0 to more. This increase cannot avoid 1 because of ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2024-09-23 13:58 -0400 |
| Message-ID | <519db81b-4a4d-417d-8cd2-7fef5a342efd@att.net> |
| In reply to | #631608 |
On 9/23/2024 8:57 AM, WM wrote: > On 22.09.2024 22:22, Jim Burns wrote: >> On 9/22/2024 2:37 PM, WM wrote: >>> On 22.09.2024 19:44, Jim Burns wrote: >>>> There is no point next to 0. >> >>> There is a smallest unit fraction >>> because >>> there are no >>> unit fractions without a first one >>> when counting from zero. >> >> Each visibleᵂᴹ unit.fraction ⅟k has >> a counter.example ¼⋅⅟k to its being smallest. > > Yes. Consider the point β between the visibleᵂᴹ unit.fractions and lower.bounds of the visibleᵂᴹ unit.fractions. VUnitFractionBounds ᵉᵃᶜʰ≤ β ≤ᵉᵃᶜʰ VUnitFractions ⎛ Imagine β being positive. ⎜ ⎜ ½.β is a visibleᵂᴹ.unit.fraction lower.bound ⎜ 2.β is among the visibleᵂᴹ unit.fractions. ⎜ 0 < ½.β < β < 2.β ⎜ ⎜ 2.β is among the visibleᵂᴹ unit.fractions. ⎜ For example, for some visibleᵂᴹ ⅟k ⎜ 0 < ½.β < β ≤ ⅟k < 2.β < ⅟1 ⎜ ⎜ But ¼⋅⅟k is also a visibleᵂᴹ unit.fraction, ⎜ and ¼⋅⅟k is where a visibleᵂᴹ unit.fraction ⎜ cannot be: below the bound. ⎜ 0 < ¼⋅⅟k < ½.β < β ≤ ⅟k < 2.β < ⅟1 ⎜ ⎜ ½.β is a not.bounding bound, ⎝ which is gibberish. A positive greatest.lower.bound of visibleᵂᴹ unit.fractions is gibberish. Also, any positive lower.bound of visibleᵂᴹ unit.fractions would be greater.than.greatest and also gibberish. > Therefore > the smallest unit fraction must be dark. A smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ, is positive and, if it weren't gibberish, would be a positive lower.bound of visibleᵂᴹ unit.fractions. However, a positive lower.bound, visibleᵂᴹ or darkᵂᴹ, of visibleᵂᴹ unit.fractions is gibberish. Therefore, a smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ, is gibberish. >> No positive point, unit.fraction or otherwise, >> is NOT undercut by some visible unit fraction. > > Wrong. > NUF(x) grows from 0 to more. > This increase cannot avoid 1 How to avoid 1 0 < ⅟⌈2+⅟x⌉ < ⅟⌈1+⅟x⌉ < x > because > of ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. ∀n ∈ ℕ: 1/n ≠ 0 0 is the point between points with no unit.fractions below and points r which, for each countable.to k there are more.than.k below ⎛ ∀ᴿr > 0: ⎜ ∀k ∈ Nᵈᵉᶠ: ⎝ 0 < ⅟⌈k+1+⅟x⌉ < ⅟⌈1+⅟x⌉ < x
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2024-09-24 21:28 +0200 |
| Message-ID | <6704347e-2f99-40f2-887f-de93f6fdd659@tha.de> |
| In reply to | #631611 |
On 23.09.2024 19:58, Jim Burns wrote: > On 9/23/2024 8:57 AM, WM wrote: > a smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ, > is gibberish. But the increase of NUF(x) from 0 to infinity without intermediate steps is not gibberish? Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2024-09-24 16:19 -0400 |
| Message-ID | <d10dbfab-9235-4fcd-a892-b407029e8f1d@att.net> |
| In reply to | #631629 |
On 9/24/2024 3:28 PM, WM wrote: > On 23.09.2024 19:58, Jim Burns wrote: >> On 9/23/2024 8:57 AM, WM wrote: >> a smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ, >> is gibberish. > > But > the increase of NUF(x) from 0 to infinity > without intermediate steps > is not gibberish? Anything which can be reached by intermediate steps is not infinite. (You (WM) apparently mean something different.) Thus increasing NUF(x) from 0 to infinity WITH intermediate steps is gibberish, in the same way in which a right triangle without a right angle is gibberish. Of many suitable definitions of natural numbers, one is: they are well.ordered (subsets minimummed or empty) they continue (have successors) they are reached by a step (≠0 have predecessors) The natural numbers are our Paradigm of Finite. There is no first unreachable natural number. By that and by its well.order, there is no unreachable natural number. ω is not a natural number. ⎛ Each before ω can be reached. ⎝ Each which can be reached is before ω. If ω-1 existed such that (ω-1)+1 = ω then ω could be reached and w+1 could be reached, even though not.before ω But that's not ω ω-1 does not exist in the same way in which four.cornered.triangles do not exist. They are gibberish, descriptions describing nothing.
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2024-09-24 22:37 +0200 |
| Message-ID | <8b3e744d-3419-40c3-a7c6-fe59edd528a9@tha.de> |
| In reply to | #631635 |
On 24.09.2024 22:19, Jim Burns wrote: > On 9/24/2024 3:28 PM, WM wrote: > Thus > increasing NUF(x) from 0 to infinity > WITH intermediate steps > is gibberish, The only alternative would by infinitely many unit fractions at one point. That is not gibberish but wrong. > > Of many suitable definitions of natural numbers, > one is: > they are well.ordered (subsets minimummed or empty) > they continue (have successors) > they are reached by a step (≠0 have predecessors) > > The natural numbers are our Paradigm of Finite. > > There is no first unreachable natural number. The natural numbers n belonging to the first infinitely many unit fractions 1/n, i.e. there where NUF(x) increases at one point from 0 to infinity, cannot be distinguished in your opinion. Thus they are unreachable. > By that and by its well.order, > there is no unreachable natural number. > > ω is not a natural number. > ⎛ Each before ω can be reached. > ⎝ Each which can be reached is before ω. > > If ω-1 existed such that (ω-1)+1 = ω > then ω could be reached If ω-1 could be seen. But it cannot. Regards, WM
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2024-09-25 00:59 -0400 |
| Message-ID | <851e9929-8ab7-49d1-b478-e65c61fba2e3@att.net> |
| In reply to | #631639 |
On 9/24/2024 4:37 PM, WM wrote: > On 24.09.2024 22:19, Jim Burns wrote: >> On 9/24/2024 3:28 PM, WM wrote: >>> On 23.09.2024 19:58, Jim Burns wrote: >>>> On 9/23/2024 8:57 AM, WM wrote: >>>> a smallest unit.fraction, visibleᵂᴹ or darkᵂᴹ, >>>> is gibberish. >>> >>> But >>> the increase of NUF(x) from 0 to infinity >>> without intermediate steps is not gibberish? >> >> Anything which >> can be reached by intermediate steps >> is not infinite. >> (You (WM) apparently mean something different.) >> >> Thus >> increasing NUF(x) from 0 to infinity >> WITH intermediate steps >> is gibberish, > > The only alternative would by > infinitely many unit fractions at one point. The correct (different) alternative is: infinitely.many unit.fractions at one point per unit.fraction, with infinitely.many points in all. Although no more than finitely.many points can be stepped.through end.to.end we don't require these points to do more than _exist_ More.than.finitely.many can _exist_ > The only alternative would by > infinitely many unit fractions at one point. > That is not gibberish but wrong. Each positive point δ, visibleᵂᴹ or darkᵂᴹ, is undercut by a visibleᵂᴹ.unit.fraction The only alternative is gibberish. ⎛ Assume δ is positive and not.undercut. ⎜ ⎜ β is between ⎜ points.undercut > β and points.not.undercut < β ⎜ ⎜ β ≥ δ > 0 ⎜ ⎜ 2⋅β > β ⎜ 2⋅β is undercut ⎜ 2⋅β > ⅟k ∈ ⅟ℕdef ⎜ ½⋅β > ¼⋅⅟k ∈ ⅟ℕdef ⎜ ½⋅β is undercut. ⎜ ⎜ However, ⎜ ½⋅β < β ⎜ ½⋅β is not.undercut ⎜ ⎜ "½⋅β is undercut and not.undercut" ⎝ is gibberish. > The only alternative would by > infinitely many unit fractions at one point. > That is not gibberish but wrong. Each positive.point, visibleᵂᴹ or darkᵂᴹ, is undercut by a visibleᵂᴹ.unit fraction Each visibleᵂᴹ.unit.fraction is undercut by more than.k unit.fractions, at one point per unit.fraction, where k is a countable.to number. Each positive point, visibleᵂᴹ or darkᵂᴹ, is undercut by more.than.finitely.many (infinitely.many) visibleᵂᴹ unit.fractions. The only alternative is gibberish. >> Of many suitable definitions of natural numbers, >> one is: >> they are well.ordered (subsets minimummed or empty) >> they continue (have successors) >> they are reached by a step (≠0 have predecessors) >> >> The natural numbers are our Paradigm of Finite. >> >> There is no first unreachable natural number. >> By that and by its well.order, >> there is no unreachable natural number. > > The natural numbers n belonging to > the first infinitely many unit fractions 1/n, i.e. > there where NUF(x) increases at one point > from 0 to infinity, > cannot be distinguished in your opinion. > Thus they are unreachable. 1. Describe 'reachable'. 2. Observe that infinitely.many (our 'infinitely.many', not what you think it is) is not what that is, is not reachable. ⎛ A finite ordered set begins and ends, or it is empty. ⎝ Each of its subsets begins and ends, or it is empty. In a finite ordered set for each split, the foresplit ends and, in one step more, the hindsplit begins. In a finite ordered set, for each split, the hindsplit _can be reached_ from the foresplit. To insist that /1 can be reached from 0 unit.fraction by unit.fraction is to insist that the unit fractions are finitely.many. To insist they are is gibberish, and it can be (has been) shown to be gibberish. >> By that and by its well.order, >> there is no unreachable natural number. >> >> ω is not a natural number. >> ⎛ Each before ω can be reached. >> ⎝ Each which can be reached is before ω. >> >> If ω-1 existed such that (ω-1)+1 = ω >> then ω could be reached > > If ω-1 could be seen. But it cannot. ω-1 is gibberish, seen or unseen.
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2024-09-25 17:51 +0200 |
| Message-ID | <vd1bis$3njbp$7@dont-email.me> |
| In reply to | #631646 |
On 25.09.2024 06:59, Jim Burns wrote: > On 9/24/2024 4:37 PM, WM wrote: >>> Thus >>> increasing NUF(x) from 0 to infinity >>> WITH intermediate steps >>> is gibberish, >> >> The only alternative would by >> infinitely many unit fractions at one point. > > The correct (different) alternative is: > infinitely.many unit.fractions > at one point per unit.fraction, That means NUF increases by 1 at every point occupied by a unit fraction. > with infinitely.many points in all. NUF(x) distinguishes all points. > Although > no more than finitely.many points > can be stepped.through end.to.end > we don't require these points to do more than _exist_ > > More.than.finitely.many can _exist_ Yes, but they are dark. NUF increases. At no point it can increase by more than 1. Even if most mathematicians are far too stupid to understand this, I will repeat it on and on, maybe that sometime some will get it. Regards, WM
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| From | joes <noreply@example.org> |
|---|---|
| Date | 2024-09-25 16:39 +0000 |
| Message-ID | <57dcb3994f147ebe5799308cad2ae1c8ac57e891@i2pn2.org> |
| In reply to | #631660 |
Am Wed, 25 Sep 2024 17:51:56 +0200 schrieb WM: > On 25.09.2024 06:59, Jim Burns wrote: > > On 9/24/2024 4:37 PM, WM wrote: > > >>> Thus increasing NUF(x) from 0 to infinity WITH intermediate steps > >>> is gibberish, > > The correct (different) alternative is: infinitely.many > > unit.fractions at one point per unit.fraction, > That means NUF increases by 1 at every point occupied by a unit > fraction. Thus it increases to infinity at every positive point. > > with infinitely.many points in all. > NUF(x) distinguishes all points. How does it distinguish dark points? > > Although no more than finitely.many points can be stepped.through > > end.to.end we don't require these points to do more than _exist_ > > More.than.finitely.many can _exist_ > Yes, but they are dark. > NUF increases. At no point it can increase by more than 1. Right, and there is no point "next to" 0, so it doesn't actually "increase" by your not-definition at 0. > Even if most mathematicians are far too stupid to understand this, I > will repeat it on and on, maybe that sometime some will get it. You should try explaining it a different way. -- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math: It is not guaranteed that n+1 exists for every n.
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