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Groups > sci.math > #639398 > unrolled thread
| Started by | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| First post | 2025-07-30 19:29 +0200 |
| Last post | 2025-08-09 07:35 -0700 |
| Articles | 20 on this page of 268 — 10 participants |
Back to article view | Back to sci.math
Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-30 19:29 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-07-30 19:09 +0000
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-07-30 14:03 -0700
Re: Conquer the Binary Tree FromTheRafters <FTR@nomail.afraid.org> - 2025-07-30 17:17 -0400
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 16:04 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 17:34 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-07-31 15:53 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 18:56 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-01 18:23 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-01 19:44 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 12:40 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 11:15 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 11:33 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 14:54 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 12:59 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 13:03 +0000
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-02 12:51 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 22:46 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-02 20:20 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-02 20:39 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-03 12:55 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-03 13:04 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 12:37 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-04 12:22 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 21:29 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-04 12:41 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 21:44 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-04 12:52 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 22:34 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-05 15:44 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-03 13:06 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 12:39 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-04 14:29 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 16:45 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-04 20:19 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 22:37 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-05 08:22 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-05 12:10 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-04 20:36 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-04 22:45 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-05 08:28 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-05 12:16 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-05 21:41 +0000
Re: Conquer the Binary Tree FromTheRafters <FTR@nomail.afraid.org> - 2025-08-05 18:41 -0400
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-05 16:23 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 19:16 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-05 15:39 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-05 15:48 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-05 14:13 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-05 16:30 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-05 17:09 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-05 17:37 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-05 19:56 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-05 19:21 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-05 22:01 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-05 21:33 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 12:10 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 19:11 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:17 -0700
Re: Conquer the Binary Tree FromTheRafters <FTR@nomail.afraid.org> - 2025-08-06 19:25 -0400
Re: Conquer the Binary Tree FromTheRafters <FTR@nomail.afraid.org> - 2025-08-06 19:29 -0400
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:42 -0700
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-06 12:43 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 16:56 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-06 16:59 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 19:34 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-06 20:12 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-07 19:06 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-07 21:20 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-08 20:39 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:23 -0700
Re: Conquer the Binary Tree Ben Bacarisse <ben@bsb.me.uk> - 2025-08-10 23:31 +0100
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 01:38 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 02:02 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 16:25 +0200
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-10 21:37 -0700
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-10 21:50 -0700
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-11 12:28 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 16:05 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 15:56 +0200
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-12 19:40 -0700
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 17:02 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 22:24 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 22:57 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 00:27 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 15:20 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 15:10 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-12 13:16 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 16:24 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-12 15:27 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 17:59 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-12 15:30 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 19:03 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-06 17:46 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-06 18:00 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 22:35 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:38 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-07 17:37 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-07 18:20 +0000
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-07 12:48 -0700
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-07 22:03 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-07 22:43 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-07 21:01 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-08 14:23 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-08 13:00 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-08 22:41 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-08 20:47 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-08 22:53 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-09 15:15 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-09 15:10 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-08 20:53 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-09 15:26 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-09 13:37 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-09 18:32 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-09 11:10 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-08 14:32 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-09 15:13 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-09 11:08 -0700
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-09 11:13 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-15 22:21 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-07 22:32 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-07 13:47 -0700
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-08 00:50 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-07 16:53 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-08 00:25 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-09 11:11 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-10 15:08 +0200
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-10 07:51 -0700
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-10 08:08 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-10 12:56 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 15:44 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-11 12:37 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 16:16 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-12 14:04 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 16:40 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 16:41 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-12 15:28 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 17:56 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 18:15 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 18:17 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 21:58 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 22:45 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-13 16:53 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 18:11 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-12 17:15 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 22:19 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 22:35 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-13 16:58 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-13 17:01 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-13 15:06 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 00:24 +0200
Re: Conquer the Binary Tree Hugh Kalambetov <ahuebbl@htlhkm.ru> - 2025-08-14 09:34 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 13:00 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-14 12:33 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 15:01 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-14 13:40 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 16:08 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-14 14:18 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 14:59 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-15 13:59 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 17:21 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 17:29 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 21:30 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-15 13:23 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 18:03 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-15 16:45 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 18:52 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-16 00:10 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-15 22:25 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-16 13:57 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-16 13:55 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-16 14:26 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-15 15:00 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 17:27 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-13 16:48 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-13 16:13 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-13 16:23 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-13 19:10 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 14:38 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-14 12:42 +0000
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-14 15:33 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 15:04 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-15 13:38 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 19:01 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-15 10:04 -0700
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-15 17:36 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-16 13:46 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-16 12:11 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-16 14:29 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-16 14:27 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-16 18:25 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-17 06:06 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-17 12:44 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-16 16:54 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-16 17:01 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-16 18:29 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-17 12:40 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-16 14:24 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 14:24 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-14 15:42 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 15:37 +0200
Re: Conquer the Binary Tree joes <noreply@example.org> - 2025-08-13 17:37 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 14:51 +0200
Re: Conquer the Binary Tree FromTheRafters <FTR@nomail.afraid.org> - 2025-08-14 11:02 -0400
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-14 11:23 -0700
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 00:43 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 00:57 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 14:56 +0200
Re: Conquer the Binary Tree Alan Mackenzie <acm@muc.de> - 2025-08-14 13:09 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-14 13:12 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 17:54 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 17:57 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 18:06 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-14 15:55 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 17:43 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 17:56 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-14 18:03 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 01:10 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 17:55 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-15 16:03 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 18:44 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-15 18:58 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-15 23:45 +0200
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-15 20:52 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-15 09:57 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-16 14:08 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-16 13:48 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-12 17:04 -0700
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 16:44 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 17:16 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 17:18 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 17:28 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 17:42 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 01:57 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 01:57 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-11 18:38 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 22:42 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-12 15:16 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-11 22:47 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 02:00 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-12 02:01 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-07 00:11 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:35 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 22:19 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:38 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:28 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-06 16:19 -0700
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-08-05 15:47 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-06 19:19 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-06 17:31 +0000
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-07 00:58 +0200
Re: Conquer the Binary Tree Moebius <invalid@example.invalid> - 2025-08-07 00:58 +0200
Ben Bacarisse's "debunking" attempt WM <wolfgang.mueckenheim@tha.de> - 2025-08-18 16:07 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 15:03 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 13:17 +0000
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-02 13:24 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 19:39 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-08-02 20:12 +0200
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 15:28 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-07-31 13:35 +0000
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 16:49 +0200
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-07-31 14:53 +0000
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-07-31 11:52 -0700
Re: Conquer the Binary Tree WM <wolfgang.mueckenheim@tha.de> - 2025-07-31 22:55 +0200
Re: Conquer the Binary Tree "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-07-31 13:58 -0700
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-09 07:11 -0700
Re: Conquer the Binary Tree Python <jp@python.invalid> - 2025-08-09 14:15 +0000
Re: Conquer the Binary Tree Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-08-09 07:35 -0700
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2025-08-07 22:32 +0200 |
| Message-ID | <10732ga$7vta$1@dont-email.me> |
| In reply to | #639524 |
On 07.08.2025 20:20, Alan Mackenzie wrote: > WM <wolfgang.mueckenheim@tha.de> wrote: > All fractions can be named, and all get indexed. Naming is done by exchange of X and O. > That's what Cantor > demonstrated. He did so for definable numbers not knowing that most numbers are undefinable. This is proved by the O's. > If you _really_ believe this isn't the case, meet Chris's > challenge and name a fraction which cannot be indexed. . I do not believe but have proved. But most dark numbers cannot be defined. > >> Nevertheless most fractions remain unindexed. > > Quatsch! Again, name a single fraction which will not be indexed. Have you understood that your example with the analytical limit of the sequence is nonsense? > >> It is impossible to shuffle one X per line over the matrix such that the >> whole matrix is covered. > > We've already discussed that to death. You have discussed the analytical limit which has nothing to do with enumerating terms. Have you understood my explanation? The terms 10^-n of the sequence (10^-n) are enumerated by n. The limit 0 is not a term and is not enumerated. It has nothing to do with Cantor's theory. The plain fact is you are wrong > here, too. The plain fact is that you have no arguments but your belief. Regards, WM
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-08-07 13:47 -0700 |
| Message-ID | <10733ca$8dd5$1@dont-email.me> |
| In reply to | #639528 |
On 8/7/2025 1:32 PM, WM wrote: > On 07.08.2025 20:20, Alan Mackenzie wrote: >> WM <wolfgang.mueckenheim@tha.de> wrote: > >> All fractions can be named, and all get indexed. > > Naming is done by exchange of X and O. > >> That's what Cantor >> demonstrated. > > He did so for definable numbers not knowing that most numbers are > undefinable. This is proved by the O's. > >> If you _really_ believe this isn't the case, meet Chris's >> challenge and name a fraction which cannot be indexed. > . > I do not believe but have proved. But most dark numbers cannot be defined. Huh? Most dark numbers? What is most of infinity? Oh my, don't tell me that WM says 1/2 is defined, but 4/2 cannot be defined. They both can be Cantor pairs with unique indexes. Is (6+9, 4+2) defined? Ahhh, WM says, well, I don't see 15 and 6, (15, 6)? Therefore they simply must be dark? Sigh... >> >>> Nevertheless most fractions remain unindexed. >> >> Quatsch! Again, name a single fraction which will not be indexed. > > Have you understood that your example with the analytical limit of the > sequence is nonsense? >> >>> It is impossible to shuffle one X per line over the matrix such that the >>> whole matrix is covered. >> >> We've already discussed that to death. > > You have discussed the analytical limit which has nothing to do with > enumerating terms. Have you understood my explanation? > > The terms 10^-n of the sequence (10^-n) are enumerated by n. The limit 0 > is not a term and is not enumerated. It has nothing to do with Cantor's > theory. > > The plain fact is you are wrong >> here, too. > > The plain fact is that you have no arguments but your belief. > > Regards, WM > >
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| From | Moebius <invalid@example.invalid> |
|---|---|
| Date | 2025-08-08 00:50 +0200 |
| Message-ID | <1073akg$ak6t$5@dont-email.me> |
| In reply to | #639524 |
Am 07.08.2025 um 20:20 schrieb Alan Mackenzie:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> All fractions that can be named get indexed.
>>
> All fractions can be named,
Indeed. If n/m is a fraction, the string consisting of n "|"s followed
by an "/" followed by m "|"s may be considered a name for n/m.
You see, Mückenheim:
1/1 is referred to by "|/|". In other words, "|/|" is a name for 1/1.
1/2 is referred to by "|/||". In other words, "|/||" is a name for 1/2.
2/1 is referred to by "||/|". In other words, "||/|" is a name for 2/1.
and so on.
[Hint @ Mückenheim: The mathematical "reality" is not
"bound"/"restricted" by the physical "reality". Mathematical objects do
not "exist" ("reside") in the physical reality. That's why mathematical
theories do NOT refer to the "physical universe". Except in your delusion.]
On the other hand,
> all get indexed. That's what Cantor demonstrated.
Indeed! Actually, this does not depend on Mückenheim's condition "can be
named". [And even if it were, your claim would still be true.]
>> Nevertheless most fractions remain unindexed.
>
> Quatsch!
Right. Complete nonsense.
Hint @ Mückenheim: If n/m is a fraction then m + ((m + n − 1) (m + n −
2))/2 is its index. Too complicated for you? <facepalm>
So there is no fraction which "remains unindexed".
.
.
.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-08-07 16:53 -0700 |
| Message-ID | <1073ea3$bfgp$1@dont-email.me> |
| In reply to | #639534 |
On 8/7/2025 3:50 PM, Moebius wrote:
> Am 07.08.2025 um 20:20 schrieb Alan Mackenzie:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>
>>> All fractions that can be named get indexed.
>>>
>> All fractions can be named,
>
> Indeed. If n/m is a fraction, the string consisting of n "|"s followed
> by an "/" followed by m "|"s may be considered a name for n/m.
>
> You see, Mückenheim:
>
> 1/1 is referred to by "|/|". In other words, "|/|" is a name for 1/1.
> 1/2 is referred to by "|/||". In other words, "|/||" is a name for 1/2.
> 2/1 is referred to by "||/|". In other words, "||/|" is a name for 2/1.
> and so on.
>
> [Hint @ Mückenheim: The mathematical "reality" is not
> "bound"/"restricted" by the physical "reality". Mathematical objects do
> not "exist" ("reside") in the physical reality. That's why mathematical
> theories do NOT refer to the "physical universe". Except in your delusion.]
>
> On the other hand,
>
>> all get indexed. That's what Cantor demonstrated.
>
> Indeed! Actually, this does not depend on Mückenheim's condition "can be
> named". [And even if it were, your claim would still be true.]
>
>>> Nevertheless most fractions remain unindexed.
>>
>> Quatsch!
>
> Right. Complete nonsense.
>
> Hint @ Mückenheim: If n/m is a fraction then m + ((m + n − 1) (m + n −
> 2))/2 is its index. Too complicated for you? <facepalm>
>
> So there is no fraction which "remains unindexed".
>
> .
> .
> .
>
WM should wrote a movie for the Dark Numbers... Oh shit, already done?
(Ghostbusters Theme)
https://youtu.be/Uvck7ItXwdc?list=RDeQNI1KfGXBA
[toc] | [prev] | [next] | [standalone]
| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-08-08 00:25 -0700 |
| Message-ID | <10748pg$hhpp$1@dont-email.me> |
| In reply to | #639534 |
On 8/7/2025 3:50 PM, Moebius wrote:
> Am 07.08.2025 um 20:20 schrieb Alan Mackenzie:
>> WM <wolfgang.mueckenheim@tha.de> wrote:
>
>>> All fractions that can be named get indexed.
>>>
>> All fractions can be named,
>
> Indeed. If n/m is a fraction, the string consisting of n "|"s followed
> by an "/" followed by m "|"s may be considered a name for n/m.
>
> You see, Mückenheim:
>
> 1/1 is referred to by "|/|". In other words, "|/|" is a name for 1/1.
> 1/2 is referred to by "|/||". In other words, "|/||" is a name for 1/2.
> 2/1 is referred to by "||/|". In other words, "||/|" is a name for 2/1.
> and so on.
>
> [Hint @ Mückenheim: The mathematical "reality" is not
> "bound"/"restricted" by the physical "reality". Mathematical objects do
> not "exist" ("reside") in the physical reality. That's why mathematical
> theories do NOT refer to the "physical universe". Except in your delusion.]
>
> On the other hand,
>
>> all get indexed. That's what Cantor demonstrated.
>
> Indeed! Actually, this does not depend on Mückenheim's condition "can be
> named". [And even if it were, your claim would still be true.]
>
>>> Nevertheless most fractions remain unindexed.
>>
>> Quatsch!
>
> Right. Complete nonsense.
>
> Hint @ Mückenheim: If n/m is a fraction then m + ((m + n − 1) (m + n −
> 2))/2 is its index. Too complicated for you? <facepalm>
>
> So there is no fraction which "remains unindexed".
If WM ever finally gets it, the dark numbers might sing the following song:
(Thriller)
https://youtu.be/Z85lxckrtzg?list=RDeQNI1KfGXBA
lo. ;^)
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-08-09 11:11 -0700 |
| Message-ID | <107830e$1eamj$6@dont-email.me> |
| In reply to | #639522 |
On 8/7/2025 8:37 AM, WM wrote: > On 07.08.2025 01:38, Chris M. Thomasson wrote: >> On 8/6/2025 1:35 PM, WM wrote: > >>> Every matrix contains O's, i.e. not indexed fractions. >> >> Name a fraction, aka a Cantor Pair in the form of (x, y) as (x/y) that >> is not indexed? >> > All fractions that can be named get indexed. > Nevertheless most fractions remain unindexed. Wow! Any cantor pair (x, y) can be indexed. The fraction (x/y) is just a way to show a fraction from any cantor pair. > It is impossible to shuffle one X per line over the matrix such that the > whole matrix is covered. > > Regards, WM >
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2025-08-10 15:08 +0200 |
| Message-ID | <107a5kk$1tg46$1@dont-email.me> |
| In reply to | #639569 |
On 09.08.2025 20:11, Chris M. Thomasson wrote: > On 8/7/2025 8:37 AM, WM wrote: >> All fractions that can be named get indexed. >> Nevertheless most fractions remain unindexed. > > Wow! Any cantor pair (x, y) can be indexed. Yes. > The fraction (x/y) is just a > way to show a fraction from any cantor pair. Alas there are, according to Cantor, |ℕ| natural numbers. Can all be smaller than |ℕ|/2? Hardly. > >> It is impossible to shuffle one X per line over the matrix such that >> the whole matrix is covered. The first column containing all natural numbers is infinite. But all other columns are just as long as the first. Therefore it is impossible to attach a natural number to every matrix element. Regards, WM
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2025-08-10 07:51 -0700 |
| Message-ID | <5RicnUeqldppLAX1nZ2dnZfqnPidnZ2d@giganews.com> |
| In reply to | #639574 |
On 08/10/2025 06:08 AM, WM wrote: > On 09.08.2025 20:11, Chris M. Thomasson wrote: >> On 8/7/2025 8:37 AM, WM wrote: > >>> All fractions that can be named get indexed. >>> Nevertheless most fractions remain unindexed. >> >> Wow! Any cantor pair (x, y) can be indexed. > > Yes. > >> The fraction (x/y) is just a way to show a fraction from any cantor pair. > > Alas there are, according to Cantor, |ℕ| natural numbers. Can all be > smaller than |ℕ|/2? Hardly. >> >>> It is impossible to shuffle one X per line over the matrix such that >>> the whole matrix is covered. > > The first column containing all natural numbers is infinite. But all > other columns are just as long as the first. Therefore it is impossible > to attach a natural number to every matrix element. > > Regards, WM > > > For an echo chamber, 'tis pretty big. Whether writing "'tis" for "it is" emphasizes the verb rather than subject, goes to show language has its meanings. Yeah, a lot of time "that" goes a long way to establish meaning, yet these days people can't even be bothered to include their commas, each omission of which is a little loss of meaning. Don't mean much. Another usual example of an inductive impasse readily dispatched with analytical bridges in the overall deductive, the wider deductive and ab-ductive if you will yet that's a kind of deductive, inference, once again we see there's a bridge of Zeno an invincible going-forwarder yet may not cross. That, ....
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2025-08-10 08:08 -0700 |
| Message-ID | <FrOdnVyg_OdBKAX1nZ2dnZfqnPGdnZ2d@giganews.com> |
| In reply to | #639575 |
On 08/10/2025 07:51 AM, Ross Finlayson wrote: > On 08/10/2025 06:08 AM, WM wrote: >> On 09.08.2025 20:11, Chris M. Thomasson wrote: >>> On 8/7/2025 8:37 AM, WM wrote: >> >>>> All fractions that can be named get indexed. >>>> Nevertheless most fractions remain unindexed. >>> >>> Wow! Any cantor pair (x, y) can be indexed. >> >> Yes. >> >>> The fraction (x/y) is just a way to show a fraction from any cantor >>> pair. >> >> Alas there are, according to Cantor, |ℕ| natural numbers. Can all be >> smaller than |ℕ|/2? Hardly. >>> >>>> It is impossible to shuffle one X per line over the matrix such that >>>> the whole matrix is covered. >> >> The first column containing all natural numbers is infinite. But all >> other columns are just as long as the first. Therefore it is impossible >> to attach a natural number to every matrix element. >> >> Regards, WM >> >> >> > > For an echo chamber, 'tis pretty big. > > > > Whether writing "'tis" for "it is" emphasizes the verb rather than > subject, goes to show language has its meanings. > > > Yeah, a lot of time "that" goes a long way to establish meaning, > yet these days people can't even be bothered to include their commas, > each omission of which is a little loss of meaning. > > Don't mean much. > > > Another usual example of an inductive impasse readily dispatched > with analytical bridges in the overall deductive, the wider deductive > and ab-ductive if you will yet that's a kind of deductive, inference, > once again we see there's a bridge of Zeno an invincible going-forwarder > yet may not cross. > > That, .... > > Between writing that and writing this, I found a few words in Quine's "Word & Object" with regards to "that", about any differences between "propositions", and, "eternal sentences", as with regards to whether for Quine there's antything like an, "eternal basic text", seems there is. Wouldn't that make him an avowed strong mathematical platonist, of a sort?
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-08-10 12:56 -0700 |
| Message-ID | <107atib$23uqe$1@dont-email.me> |
| In reply to | #639574 |
On 8/10/2025 6:08 AM, WM wrote: > On 09.08.2025 20:11, Chris M. Thomasson wrote: >> On 8/7/2025 8:37 AM, WM wrote: > >>> All fractions that can be named get indexed. >>> Nevertheless most fractions remain unindexed. >> >> Wow! Any cantor pair (x, y) can be indexed. > > Yes. So, any fraction wrt (x/y) are indexed... Well, think of positive numbers for now... :^) > >> The fraction (x/y) is just a way to show a fraction from any cantor pair. > > Alas there are, according to Cantor, |ℕ| natural numbers. Can all be > smaller than |ℕ|/2? Hardly. >> >>> It is impossible to shuffle one X per line over the matrix such that >>> the whole matrix is covered. > > The first column containing all natural numbers is infinite. But all > other columns are just as long as the first. Therefore it is impossible > to attach a natural number to every matrix element. Humm... You cannot bastardize the mapping. Humm... I don't think you have ever implemented Cantor Pairing wrt going back and forth in the sense of mapping an index into a unique pair and back again? Am I right?
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2025-08-11 15:44 +0200 |
| Message-ID | <107cs3m$2j48j$1@dont-email.me> |
| In reply to | #639579 |
On 10.08.2025 21:56, Chris M. Thomasson wrote: > On 8/10/2025 6:08 AM, WM wrote: >> On 09.08.2025 20:11, Chris M. Thomasson wrote: >>> On 8/7/2025 8:37 AM, WM wrote: >> >>>> All fractions that can be named get indexed. >>>> Nevertheless most fractions remain unindexed. >>> >>> Wow! Any cantor pair (x, y) can be indexed. >> >> Yes. > > So, any fraction wrt (x/y) are indexed No. Only any Cantor pair. > I don't think you > have ever implemented Cantor Pairing wrt going back and forth in the > sense of mapping an index into a unique pair and back again? Am I right? No. See https://www.hs-augsburg.de/~mueckenh/HI/HI11.PPT page 18. Regards, WM
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2025-08-11 12:37 +0000 |
| Message-ID | <107co6q$2u5l$2@news.muc.de> |
| In reply to | #639574 |
WM <wolfgang.mueckenheim@tha.de> wrote: > On 09.08.2025 20:11, Chris M. Thomasson wrote: >> On 8/7/2025 8:37 AM, WM wrote: >>> All fractions that can be named get indexed. >>> Nevertheless most fractions remain unindexed. >> Wow! Any cantor pair (x, y) can be indexed. > Yes. >> The fraction (x/y) is just a >> way to show a fraction from any cantor pair. > Alas there are, according to Cantor, |ℕ| natural numbers. Can all be > smaller than |ℕ|/2? Hardly. Maybe, just maybe, |ℕ|/2 isn't even defined. >>> It is impossible to shuffle one X per line over the matrix such that >>> the whole matrix is covered. > The first column containing all natural numbers is infinite. But all > other columns are just as long as the first. Therefore it is impossible > to attach a natural number to every matrix element. You are wrong there, and you know it. Your utterance of such blatant nonsense explains the contempt in which you are held here. > Regards, WM -- Alan Mackenzie (Nuremberg, Germany).
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2025-08-11 16:16 +0200 |
| Message-ID | <107ctve$2iuu8$3@dont-email.me> |
| In reply to | #639590 |
On 11.08.2025 14:37, Alan Mackenzie wrote: > WM <wolfgang.mueckenheim@tha.de> wrote: >> Alas there are, according to Cantor, |ℕ| natural numbers. Can all be >> smaller than |ℕ|/2? Hardly. > > Maybe, just maybe, |ℕ|/2 isn't even defined. If |ℕ| is defined as an integer or whole number, then there must be as many natural numbers. Otherwise |ℕ| and ℕ would be a lie only. Not the definition is lacking. But the numbers between |ℕ|/2 and |ℕ| are dark. > >>>> It is impossible to shuffle one X per line over the matrix such that >>>> the whole matrix is covered. > >> The first column containing all natural numbers is infinite. But all >> other columns are just as long as the first. Therefore it is impossible >> to attach a natural number to every matrix element. > > You are wrong there, and you know it. Do you accept analysis? > Your utterance of such blatant > nonsense explains the contempt in which you are held here. That is based on the stupidity of the readers her. They claim that infinite set theory is the basis of mathematics but don't accept the results of mathematics, for instance the share of indices n/1 within the infinite matrix. The number of indices n/1 in the first column of an n*n-matrix is n. Its share in the matrix is n/n^2. Here the limit tells us about the share of enumerated fractions in the infinite matrix: lim(n-->oo) n/n^2 = 0. Regards, WM
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2025-08-12 14:04 +0000 |
| Message-ID | <107fhlf$2k43$2@news.muc.de> |
| In reply to | #639595 |
WM <wolfgang.mueckenheim@tha.de> wrote: > On 11.08.2025 14:37, Alan Mackenzie wrote: >> WM <wolfgang.mueckenheim@tha.de> wrote: >>> Alas there are, according to Cantor, |ℕ| natural numbers. Can all be >>> smaller than |ℕ|/2? Hardly. >> Maybe, just maybe, |ℕ|/2 isn't even defined. > If |ℕ| is defined as an integer or whole number, .... It's not. > .... then there must be as many natural numbers. Otherwise |ℕ| and ℕ > would be a lie only. I'll accept your expertise on lies. But as a hint, "as many" doesn't mean exactly the same for infinite sets as finite sets. > Not the definition is lacking. But the numbers between |ℕ|/2 and |ℕ| are > dark. There are no "dark numbers". Their non-existence has been proven on this newsgroup at least twice. And, as already implied, |ℕ|/2 is not coherently defined. >>>>> It is impossible to shuffle one X per line over the matrix such that >>>>> the whole matrix is covered. >>> The first column containing all natural numbers is infinite. But all >>> other columns are just as long as the first. Therefore it is impossible >>> to attach a natural number to every matrix element. >> You are wrong there, and you know it. > Do you accept analysis? Not from you, I wouldn't. >> Your utterance of such blatant >> nonsense explains the contempt in which you are held here. > That is based on the stupidity of the readers here. They claim that > infinite set theory is the basis of mathematics but don't accept the > results of mathematics, .... We don't accept false pseudo-mathematics, as propounded by mathematically ill-educated cranks. > .... for instance the share of indices n/1 within the infinite matrix. > The number of indices n/1 in the first column of an n*n-matrix is n. > Its share in the matrix is n/n^2. Here the limit tells us about the > share of enumerated fractions in the infinite matrix: lim(n-->oo) n/n^2 > = 0. Well, so what? The proportion of these numbers counted in that way may tend to zero, their absolute number in the limit is countably infinite. As is the count of all these numbers. They can be put into a 1-1 correspondence, hence they are "the same" size. > Regards, WM -- Alan Mackenzie (Nuremberg, Germany).
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| From | Moebius <invalid@example.invalid> |
|---|---|
| Date | 2025-08-12 16:40 +0200 |
| Message-ID | <107fjpa$38olk$1@dont-email.me> |
| In reply to | #639621 |
Am 12.08.2025 um 16:04 schrieb Alan Mackenzie:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> If |ℕ| is defined as an integer or whole number, ....
>
> It's not.
Crank Wolfgang Mückenheim is using CANTORs terminology here. CANTOR
considered his infinite numbers (if ordinals/cardinals, I can't say) as
an EXTENTION of the finite "whole numbers".
Of course, these days such a terminology would lead to confusion, you see.
>> Not the definition is lacking. But the numbers between |ℕ|/2 and |ℕ| are
>> dark.
"[WM's] conclusions are based on the sloppiness of his notions,
his inability of giving precise definitions, his fundamental
misunderstanding of elementary mathematical concepts, and sometimes,
as the late Dik Winter remarked [...], on nothing at all."
--Franz Lemmermeyer
On the other hand, after defining "|ℕ|/2" in a reasonable way, say:
|ℕ|/2 := the cardinal number k such that k * 2 = |ℕ| (*)
we get that |ℕ|/2 = |ℕ|, since |ℕ| * 2 = |ℕ| (and there is no OTHER
cardinal number k such that k * 2 = |ℕ|).
> There are no "dark numbers". Their non-existence has been proven on
> this newsgroup at least twice.
Yeah, and (presupposing the definition (*)) it's even in agreement with
WM's claim that "the numbers between |ℕ|/2 and |ℕ| are dark." After all,
there ARE NO numbers "(strictly) between" |ℕ|/2 and |ℕ|.
Of course ... WM's "definition" of /dark/ is dark itself. But that's not
relevant in this case. After all, the elements in the empty set have ANY
property there is.
.
.
.
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| From | WM <wolfgang.mueckenheim@tha.de> |
|---|---|
| Date | 2025-08-12 16:41 +0200 |
| Message-ID | <107fjq5$38o9n$7@dont-email.me> |
| In reply to | #639621 |
On 12.08.2025 16:04, Alan Mackenzie wrote: > WM <wolfgang.mueckenheim@tha.de> wrote: >> On 11.08.2025 14:37, Alan Mackenzie wrote: >>> WM <wolfgang.mueckenheim@tha.de> wrote: > >>>> Alas there are, according to Cantor, |ℕ| natural numbers. Can all be >>>> smaller than |ℕ|/2? Hardly. > >>> Maybe, just maybe, |ℕ|/2 isn't even defined. > >> If |ℕ| is defined as an integer or whole number, .... > > It's not. Cantor: "ich nenne deren Ordnungstypen allgemein reale ganze Zahlen." >> Not the definition is lacking. But the numbers between |ℕ|/2 and |ℕ| are >> dark. > > There are no "dark numbers". You have not yet grasped them. > Their non-existence has been proven on this > newsgroup at least twice. Liar. >> .... for instance the share of indices n/1 within the infinite matrix. >> The number of indices n/1 in the first column of an n*n-matrix is n. >> Its share in the matrix is n/n^2. Here the limit tells us about the >> share of enumerated fractions in the infinite matrix: lim(n-->oo) n/n^2 >> = 0. > > Well, so what? The proportion of these numbers counted in that way may > tend to zero, They will never cover the matrix. > their absolute number in the limit is countably infinite. That nonsense notion may fit, but they will never cover the matrix. > As is the count of all these numbers. They can be put into a 1-1 > correspondence, hence they are "the same" size. Not according to mathematical analysis. Regards, WM >
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2025-08-12 15:28 +0000 |
| Message-ID | <107fmjb$2k43$3@news.muc.de> |
| In reply to | #639624 |
WM <wolfgang.mueckenheim@tha.de> wrote: > On 12.08.2025 16:04, Alan Mackenzie wrote: >> WM <wolfgang.mueckenheim@tha.de> wrote: >>> On 11.08.2025 14:37, Alan Mackenzie wrote: >>>> WM <wolfgang.mueckenheim@tha.de> wrote: >>>>> Alas there are, according to Cantor, |ℕ| natural numbers. Can all be >>>>> smaller than |ℕ|/2? Hardly. >>>> Maybe, just maybe, |ℕ|/2 isn't even defined. >>> If |ℕ| is defined as an integer or whole number, .... >> It's not. > Cantor: "ich nenne deren Ordnungstypen allgemein reale ganze Zahlen." What's that got to do with it? |ℕ| is not an integer. >>> Not the definition is lacking. But the numbers between |ℕ|/2 and |ℕ| are >>> dark. >> There are no "dark numbers". > You have not yet grasped them. In as much as you have defined them, yes I have. The two pertinent things about a "dark number" are (i) it is an integer; (ii) its value cannot be pinned down in any way. >> Their non-existence has been proven on this newsgroup at least twice. > Liar. Please, I don't lie on Usenet, ever. The proof I gave runs as follows. Suppose the "dark numbers" are a non-empty subset of the integers, from (i) above. Then this subset, as any non-empty subset of the integers, has a least member. This least member is now defined, pinned down. Therefore, by (ii) above, it can't be a "dark number". This is a contradiction. Thus there cannot be such "dark numbers". >>> .... for instance the share of indices n/1 within the infinite matrix. >>> The number of indices n/1 in the first column of an n*n-matrix is n. >>> Its share in the matrix is n/n^2. Here the limit tells us about the >>> share of enumerated fractions in the infinite matrix: lim(n-->oo) n/n^2 >>> = 0. >> Well, so what? The proportion of these numbers counted in that way may >> tend to zero, > They will never cover the matrix. Of course they can. There are an uncountably infinite number of them, just as there are an uncountably infinite number of cells in the matrix. Thus there is a 1-1 correspondence between them, i.e. a covering. >> their absolute number in the limit is countably infinite. > That nonsense notion may fit, but they will never cover the matrix. Moebius has demonstrated such a covering explicitly. >> As is the count of all these numbers. They can be put into a 1-1 >> correspondence, hence they are "the same" size. > Not according to mathematical analysis. You mean, not according to cranky pseudo-mathematical "analysis". > Regards, WM -- Alan Mackenzie (Nuremberg, Germany).
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| From | Moebius <invalid@example.invalid> |
|---|---|
| Date | 2025-08-12 17:56 +0200 |
| Message-ID | <107fo7b$3b8pb$1@dont-email.me> |
| In reply to | #639626 |
Am 12.08.2025 um 17:28 schrieb Alan Mackenzie:
>> They will never cover the matrix. (WM)
>
> Of course they can. There are an uncountably << countably?
> infinite number of them,just as there are an uncountably << countably?
> infinite number of cells in the matrix.
> Thus there is a 1-1 correspondence between them, i.e. a covering.
>> That nonsense notion may fit, but they will never cover the matrix.
>
> Moebius has demonstrated such a covering explicitly.
Even a PROPER SUBSET of the set of natural numbers suffice to "cover"
the "matrix".
We just may consider the "matrix" (a_n,m)_(n,m e IN) defind with
a_n,m = 2^n * 3^m (for all n,m e IN).
It's easy to show that for any n,m,n',m' with (n,m) =/= (n',m'): a_n,m
=/= a_n',m'. (And it's clear that {2^n * 3^m e IN : n,m e IN} is a
proper subset of IN.)
It seems to me that Mückenheim must reject most of basic modern maths
stuff (as well as logical and/or coherent thinking, of course) in his
crusade against "set theory".
"One wonders by what [Mückenheim] would like to replace the mathematics
created in the last 2500 years; if one takes Prof. Mückenheim seriously,
then a fitting picture for the last page of this book ["The mathematics
of infinity"] would be the Ishango bone." (Franz Lemmermeyer)
https://en.wikipedia.org/wiki/Ishango_bone
.
.
.
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| From | Moebius <invalid@example.invalid> |
|---|---|
| Date | 2025-08-12 18:15 +0200 |
| Message-ID | <107fpbf$3b8pa$2@dont-email.me> |
| In reply to | #639628 |
Am 12.08.2025 um 17:56 schrieb Moebius:
> Am 12.08.2025 um 17:28 schrieb Alan Mackenzie:
>
>>> They will never cover the matrix. (WM)
>>
>> Of course they can. There are an uncountably << countably?
>
>> infinite number of them,just as there are an uncountably << countably?
>
>> infinite number of cells in the matrix.
>> Thus there is a 1-1 correspondence between them, i.e. a covering.
>
>>> That nonsense notion may fit, but they will never cover the matrix.
>>
>> Moebius has demonstrated such a covering explicitly.
>
> Even a PROPER SUBSET of the set of natural numbers suffice to "cover"
> the "matrix".
>
> We just may consider the "matrix" (a_n,m)_(n,m e IN) defind with
>
> a_n,m = 2^n * 3^m (for all n,m e IN).
>
> It's easy to show that for any n,m,n',m' with (n,m) =/= (n',m'): a_n,m
> =/= a_n',m'. (And it's clear that {2^n * 3^m e IN : n,m e IN} is a
> proper subset of IN.)
>
> It seems to me that Mückenheim must reject most of basic modern maths
> stuff (as well as logical and/or coherent thinking, of course) in his
> crusade against "set theory".
>
> "One wonders by what [Mückenheim] would like to replace the mathematics
> created in the last 2500 years; if one takes Prof. Mückenheim seriously,
> then a fitting picture for the last page of this book ["The mathematics
> of infinity"] would be the Ishango bone." (Franz Lemmermeyer)
>
> https://en.wikipedia.org/wiki/Ishango_bone
Atually, WM's "argument" woult as well concern the following TRIVIAL case:
The prime numbers will never "cover" a 1 x IN "matrix" (i.e. a
sequence). So there can't be an infinite sequence (2, 3, 5, 7, ...) of
prime numbers.
After all there are as many terms as natural numbers: p_1, p_2, p_3, ...
(in other words, the index set of an infinite sequence is IN), but there
are far less prime numbers, so HOW CAN THEY cover ALL "places" in the
sequence?!
> .
> .
> .
>
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| From | Moebius <invalid@example.invalid> |
|---|---|
| Date | 2025-08-12 18:17 +0200 |
| Message-ID | <107fpel$3b8pa$3@dont-email.me> |
| In reply to | #639628 |
Am 12.08.2025 um 17:56 schrieb Moebius:
> Am 12.08.2025 um 17:28 schrieb Alan Mackenzie:
>
>>> They will never cover the matrix. (WM)
>>
>> Of course they can. There are an uncountably << countably?
>
>> infinite number of them,just as there are an uncountably << countably?
>
>> infinite number of cells in the matrix.
>> Thus there is a 1-1 correspondence between them, i.e. a covering.
>
>>> That nonsense notion may fit, but they will never cover the matrix.
>>
>> Moebius has demonstrated such a covering explicitly.
>
> Even a PROPER SUBSET of the set of natural numbers suffice to "cover"
> the "matrix".
>
> We just may consider the "matrix" (a_n,m)_(n,m e IN) defind with
>
> a_n,m = 2^n * 3^m (for all n,m e IN).
>
> It's easy to show that for any n,m,n',m' with (n,m) =/= (n',m'): a_n,m
> =/= a_n',m'. (And it's clear that {2^n * 3^m e IN : n,m e IN} is a
> proper subset of IN.)
>
> It seems to me that Mückenheim must reject most of basic modern maths
> stuff (as well as logical and/or coherent thinking, of course) in his
> crusade against "set theory".
>
> "One wonders by what [Mückenheim] would like to replace the mathematics
> created in the last 2500 years; if one takes Prof. Mückenheim seriously,
> then a fitting picture for the last page of this book ["The mathematics
> of infinity"] would be the Ishango bone." (Franz Lemmermeyer)
>
> https://en.wikipedia.org/wiki/Ishango_bone
Atually, WM's "argument" woult as well concern the following TRIVIAL case:
The prime numbers will never "cover" a 1 x IN "matrix" (i.e. a
sequence). So there can't be an infinite sequence (2, 3, 5, 7, ...) of
prime numbers.
After all there are as many terms in a sequence as natural numbers: a_1,
a_2, a_3, ... (in other words, the index set of an infinite sequence is
IN), but there are far less prime numbers, so HOW CAN THEY cover ALL
"places" a_1, a_2, a_3, ... in the sequence?!
> .
> .
> .
>
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