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Groups > sci.logic > #210293 > unrolled thread
| Started by | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| First post | 2019-09-08 09:49 -0700 |
| Last post | 2019-09-11 14:00 -0700 |
| Articles | 20 on this page of 260 — 11 participants |
Back to article view | Back to sci.logic
Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-08 09:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-08 11:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:17 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-10 20:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:40 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-11 23:12 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 06:45 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-08 21:14 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 12:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-09 12:59 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:36 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-09 19:56 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 08:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-10 17:54 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-11 15:45 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-11 07:08 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:38 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-11 14:48 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:06 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-12 10:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-12 12:00 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 08:59 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 13:56 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 13:44 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-10 13:57 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:16 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-11 13:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 14:01 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-11 14:35 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 06:54 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 07:46 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 08:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 08:54 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 13:19 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-12 13:21 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 14:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 12:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 03:00 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 03:38 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:42 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 06:02 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:54 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 09:37 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:26 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 07:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-15 16:13 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-15 21:29 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-15 16:55 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 12:59 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 13:12 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 15:34 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-16 23:49 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-17 08:53 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:04 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 14:55 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 16:17 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 21:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:35 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:32 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:46 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 12:46 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 17:52 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-18 18:58 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:47 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 14:53 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:37 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-17 21:34 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 12:37 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-18 21:01 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 22:11 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-19 22:21 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-20 00:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-18 18:28 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-16 15:38 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Fred <Fred@nowhere.invalid> - 2019-09-16 15:53 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-16 08:43 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-16 17:51 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-16 13:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 16:02 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-15 17:04 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:44 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:09 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:28 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@invalid> - 2019-09-17 18:38 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:28 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:43 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 14:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 09:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-18 10:45 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 14:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-18 15:40 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-19 04:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-19 14:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-20 08:22 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-20 09:55 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-21 12:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-21 12:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-21 13:47 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-21 14:17 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-23 12:02 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-23 12:26 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 06:14 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 07:54 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-23 12:46 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-23 14:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-23 15:25 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-24 00:37 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:12 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 06:17 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-24 15:26 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 07:03 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:22 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 07:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 08:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? WM <mueckenh@rz.fh-augsburg.de> - 2019-09-24 09:05 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:09 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? WM <mueckenh@rz.fh-augsburg.de> - 2019-09-24 09:06 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 09:18 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 13:20 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 13:43 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-25 09:41 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-25 09:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-27 13:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-27 13:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 12:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 12:36 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 13:08 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 13:24 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-28 14:00 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-28 14:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 06:11 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 08:00 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 11:05 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 12:02 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-29 13:34 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-29 13:45 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-29 13:47 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 09:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-30 10:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 11:30 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-30 11:57 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-30 23:44 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-01 01:19 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-01 07:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-01 11:14 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-01 12:35 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-01 13:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 02:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 02:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 02:58 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 03:24 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-02 08:45 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-02 09:02 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-03 08:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-03 10:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-10-03 10:56 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-10-02 10:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-02 10:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-03 08:46 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-10-03 10:13 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-10-04 13:59 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-30 11:10 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-29 14:30 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-24 08:00 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-23 14:19 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:09 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-24 06:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-24 07:15 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-21 14:22 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Python <python@python.invalid> - 2019-09-22 03:07 +0200
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-25 20:14 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-27 13:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-18 20:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-19 04:50 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-13 12:44 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-13 12:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-12 15:36 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:38 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 12:17 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:53 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 06:24 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:30 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-09 13:08 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:44 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-14 18:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-15 02:52 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 05:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 16:49 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 13:30 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-15 13:33 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:40 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 10:46 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 10:48 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:06 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:21 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:47 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-15 17:09 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:47 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-16 13:10 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 13:25 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 13:34 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 14:31 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-18 09:26 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-16 02:39 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-16 10:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 12:08 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 01:34 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-16 13:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-17 09:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-15 02:55 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-08 22:38 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-09 13:09 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-09 13:21 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-10 03:27 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-10 08:14 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-11 02:25 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-11 13:16 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:15 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:23 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 17:03 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 13:27 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-13 00:40 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 04:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:00 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 06:24 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:37 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 06:39 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 06:45 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 09:40 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-13 14:28 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-13 14:51 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 05:14 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 02:15 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 05:49 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 15:29 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-14 08:38 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:11 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-11 15:11 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:23 +0100
Re: Can the empty set be the limit of a sequence of non-empty sets? jvr <jrennenkampff@googlemail.com> - 2019-09-12 02:08 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? George Greene <greeneg@email.unc.edu> - 2019-09-11 15:10 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Ganzhinterseher <claus.vonnesser@gmail.com> - 2019-09-12 07:29 -0700
Re: Can the empty set be the limit of a sequence of non-empty sets? Transfinite Numbers <bursejan@gmail.com> - 2019-09-11 14:00 -0700
Page 13 of 13 — ← Prev page 1 … 11 12 [13]
| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-13 06:00 -0700 |
| Message-ID | <987b77ba-e780-456d-b7af-52dee1fb80e7@googlegroups.com> |
| In reply to | #210600 |
Yes, if we accept Mückenstep:
/* WMs Fallacy */
forall n P(n) => P(N)
Then of course set theory is inconsistent.
On Friday, September 13, 2019 at 1:49:18 PM UTC+2, Ganzhinterseher wrote:
> Am Freitag, 13. September 2019 01:40:30 UTC+2 schrieb Ben Bacarisse:
> > Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>
>
> > >> lim_{n->oo} e_n(x) = 0.
> > >
> > > That is true for potential infinity (my book) and for every definable
> > > n (there are infinitely many in set theory), followed by infinitely
> > > many undefinable natnumbers.
> >
> > Oh! So in WMaths the limit function is e(x) = 0. I thought you denied
> > this.
>
> Up to every definable n this is correct. In mathematics there are only definable n. In set theory there is actual infinity, i.e., a set larger than all FISONs. Since all definable natnumbers are in FISONs, the actually infinite set must contain more than definable numbers.
> >
> > And just to be clear, you think that in "set theory" (i.e. normal
> > mathematics) there are some x ∈ N for which lim_{n->oo} e_n(x) is not 0.
> > I won't ask you to prove this -- it's just useful for people to see your
> > beliefs clearly stated.
>
> It is easy: Since all definable natnumbers are in FISONs, the actually infinite set (larger than all FISONs) must contain more than definable numbers.
> >
> > Presumably there is nothing special about the functions I picked. Can
> > you confirm that you think that in "set theory" there are no point-wise
> > limit functions because the "for every x" in the definition can never be
> > met?
>
> All limit functions are correctly described in potential infinity. The set of definable numbers in set theory is always finite without a last element, i.e., the same a the set of all natural numbers in potential infinity.
> >
>
> > >> How can there be more? Is there a natural number that is not in the
> > >> potentially infinite set N?
> > >
> > > In set theory there must be more. There is no potential infinity.
> >
> > As you say, there is no potential infinity so what on Earth did you
> > think you were asking about set theory?
>
> Since all definable natnumbers are in FISONs, the actually infinite set (larger than all FISONs) must contain more than definable numbers.
> >
> > Mathematics (what you call set theory) proves statements like
> >
> > for every x ∈ N, lim_{n->oo} e_n(x) = 0.
>
> It also proves ∀k ∈ ℕ ∩{E(k+1),E(k+2), E(k+3),...} = { } (*)
>
> Therefore for all natnumbers there must be infinitely many successors. Even the intersection of these successor sets must be infinite. Otherwise (*) would not be true for all natnumbers k.
> >
> > There are no qualifications about "purple x", "honourable x" or
> > "definable x". The proof just applies to every x ∈ N.
>
> As you see here (*), it does not. It is only believes by people who are not looking through.
>
> Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-13 06:24 -0700 |
| Message-ID | <ef5a0d21-c1bb-4816-abf2-043d1b385637@googlegroups.com> |
| In reply to | #210601 |
Am Freitag, 13. September 2019 15:00:04 UTC+2 schrieb Transfinite Numbers:
> > It also proves ∀k ∈ ℕ ∩{E(k+1),E(k+2), E(k+3),...} = { } (*)
> >
> > Therefore for all natnumbers there must be infinitely many successors. Even the intersection of these successor sets must be infinite. Otherwise (*) would not be true for all natnumbers k.
> Yes, if we accept
>
> forall n P(n) => P(N)
I do *not* claim
∀ℕ ∈ ℕ ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} = { }
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-13 06:37 -0700 |
| Message-ID | <32337a83-30ea-4113-8b79-483a4b05ad42@googlegroups.com> |
| In reply to | #210602 |
Wouldn't make any sense, since its not Mückenstep.
On Friday, September 13, 2019 at 3:25:00 PM UTC+2, Ganzhinterseher wrote:
> Am Freitag, 13. September 2019 15:00:04 UTC+2 schrieb Transfinite Numbers:
>
> > > It also proves ∀k ∈ ℕ ∩{E(k+1),E(k+2), E(k+3),...} = { } (*)
> > >
> > > Therefore for all natnumbers there must be infinitely many successors. Even the intersection of these successor sets must be infinite. Otherwise (*) would not be true for all natnumbers k.
>
> > Yes, if we accept
> >
> > forall n P(n) => P(N)
>
> I do *not* claim
>
> ∀ℕ ∈ ℕ ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} = { }
>
> Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-13 06:39 -0700 |
| Message-ID | <43406945-2358-4d99-8f55-a1ed18594a25@googlegroups.com> |
| In reply to | #210603 |
This here:
∀ℕ ∈ ℕ ...
is vacously true, if we translate the bound quantifier
∀x ∈ A ... into ∀x(x ∈ A => ...), we get this here:
∀ℕ (ℕ ∈ ℕ => ...)
But in set theory, because of regularity, x ∈ x is
always falso, so the quantifier is vacously true.
On Friday, September 13, 2019 at 3:37:14 PM UTC+2, Transfinite Numbers wrote:
> Wouldn't make any sense, since its not Mückenstep.
>
> On Friday, September 13, 2019 at 3:25:00 PM UTC+2, Ganzhinterseher wrote:
> > Am Freitag, 13. September 2019 15:00:04 UTC+2 schrieb Transfinite Numbers:
> >
> > > > It also proves ∀k ∈ ℕ ∩{E(k+1),E(k+2), E(k+3),...} = { } (*)
> > > >
> > > > Therefore for all natnumbers there must be infinitely many successors. Even the intersection of these successor sets must be infinite. Otherwise (*) would not be true for all natnumbers k.
> >
> > > Yes, if we accept
> > >
> > > forall n P(n) => P(N)
> >
> > I do *not* claim
> >
> > ∀ℕ ∈ ℕ ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} = { }
> >
> > Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-13 06:45 -0700 |
| Message-ID | <a22c43d0-ae82-462c-84f1-a0b0781b2a35@googlegroups.com> |
| In reply to | #210604 |
Am Freitag, 13. September 2019 15:40:00 UTC+2 schrieb Transfinite Numbers:
> But in set theory, because of regularity, x ∈ x is
> always falso, so the quantifier is vacously true.
Also in set theory I do not claim
∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} = { }
as you counterfactually claim.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-13 09:40 -0700 |
| Message-ID | <28c0fd42-19d7-438c-8d59-c5eb159cc898@googlegroups.com> |
| In reply to | #210606 |
Its only counterfactual versus Mückamatik,
if you would claim:
∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} <> { }
But such a claim is brain damaged, since you
cannot prove it. You can only prove it using
this fallacy here:
/* WMs Fallacy */
forall n P(n) => P(N)
On Friday, September 13, 2019 at 3:45:29 PM UTC+2, Ganzhinterseher wrote:
> Am Freitag, 13. September 2019 15:40:00 UTC+2 schrieb Transfinite Numbers:
>
> > But in set theory, because of regularity, x ∈ x is
> > always falso, so the quantifier is vacously true.
>
> Also in set theory I do not claim
>
> ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} = { }
>
> as you counterfactually claim.
>
> Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-13 14:28 -0700 |
| Message-ID | <33436ad4-e57d-4dd5-bece-c2dd6d15f674@googlegroups.com> |
| In reply to | #210626 |
Am Freitag, 13. September 2019 18:40:37 UTC+2 schrieb Transfinite Numbers:
> ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} <> { }
>
> But such a claim is brain damaged, since you
> cannot prove it.
I never claimed that. But it is what you are accusing me:
> /* WMs Fallacy */
>
> forall n P(n) => P(N)
So either you are very stupid or very dishonest or both.
Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-13 14:51 -0700 |
| Message-ID | <f66f512e-27f0-4ac1-ba4f-442b0d4e975d@googlegroups.com> |
| In reply to | #210649 |
Well you conclude from:
∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { }
That:
E(1) ∩ E(2) ∩ ... ∩ E(n) ∩ ... =/= { }
Which is fallacious reasoning. There is no
such inference rule in set theory.
On Friday, September 13, 2019 at 11:28:47 PM UTC+2, Ganzhinterseher wrote:
> Am Freitag, 13. September 2019 18:40:37 UTC+2 schrieb Transfinite Numbers:
>
> > ∩{E(ℕ+1),E(ℕ+2), E(ℕ+3),...} <> { }
> >
> > But such a claim is brain damaged, since you
> > cannot prove it.
>
> I never claimed that. But it is what you are accusing me:
>
> > /* WMs Fallacy */
> >
> > forall n P(n) => P(N)
>
> So either you are very stupid or very dishonest or both.
>
> Regards, WM
[toc] | [prev] | [next] | [standalone]
| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-14 05:14 -0700 |
| Message-ID | <62ac5e1c-d353-40f0-b228-7c70d4f9384a@googlegroups.com> |
| In reply to | #210650 |
Am Freitag, 13. September 2019 23:51:03 UTC+2 schrieb Transfinite Numbers:
> Well you conclude from:
>
> ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
>
> That:
>
> E(1) ∩ E(2) ∩ ... ∩ E(n) ∩ ... =/= { }
That is not what you accused me for: forall n P(n) => P(N). I hope you can understand this at least after having been told it.
>
> Which is fallacious reasoning.
That is the simple application of logic because there are not more than all endsegments.
> There is no
> such inference rule in set theory.
If set theory does not support this conclusion, then
(1) it has to present endsegments that are not covered by (*) and can extend all finite intersections addressed in (*).
(2) Or it has to accept dark numbers.
(3) Or it is fool's crap.
There are no other alternatives.
But it will be interesting for intelligent students to recognize this feature of set theory before having been trapped and brain-damaged by this disease.
Regards, WM
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-14 02:15 +0100 |
| Message-ID | <87blvnispc.fsf@bsb.me.uk> |
| In reply to | #210600 |
Ganzhinterseher <claus.vonnesser@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Am Freitag, 13. September 2019 01:40:30 UTC+2 schrieb Ben Bacarisse:
>> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
CONTEXT (why do you keep cutting key facts?): The e_n are a family of
functions: e_n(x) = 1 if x >= n, 0 otherwise.
>> >> lim_{n->oo} e_n(x) = 0.
>> >
>> > That is true for potential infinity (my book) and for every definable
>> > n (there are infinitely many in set theory), followed by infinitely
>> > many undefinable natnumbers.
>>
>> Oh! So in WMaths the limit function is e(x) = 0. I thought you denied
>> this.
>
> Up to every definable n this is correct.
You are being evasive! You cut the full quote. Why would you do that?.
You agreed that, in WMaths,
for every x in N, lim_{n->oo} e_n(x) = 0
and that is all the definition requires for e(x) = 0 to be the limit
function. Yet you won't say "yes" without some added mysterious
qualification.
Of course, you can change your mind. You can retract your prior
agreement that, in WMaths, lim_{n->oo} e_n(x) = 0 for every x in N, but
you are not doing that either, it seems. Ducking and diving is the
order of the day.
> In mathematics there are only definable n.
That your made-up WMaths, yes? The "mathematics" that permits e ∈ S and
S \ {e} = S to be the case, yes?
>> And just to be clear, you think that in "set theory" (i.e. normal
>> mathematics) there are some x ∈ N for which lim_{n->oo} e_n(x) is not 0.
>> I won't ask you to prove this -- it's just useful for people to see your
>> beliefs clearly stated.
>
> It is easy: Since all definable natnumbers are in FISONs, the actually
> infinite set (larger than all FISONs) must contain more than definable
> numbers.
More evasion. Please confirm that you are claiming that, in what you
call "set theory", e(x) = 0 is /not/ the point-wise limit of the
function sequence I gave.
>> Presumably there is nothing special about the functions I picked. Can
>> you confirm that you think that in "set theory" there are no point-wise
>> limit functions because the "for every x" in the definition can never be
>> met?
>
> All limit functions are correctly described in potential infinity. The
> set of definable numbers in set theory is always finite without a last
> element, i.e., the same a the set of all natural numbers in potential
> infinity.
Ha! That is how you answer a "can you confirm that..." question, is it?
I've come to accept that you try your hardest to equivocate on such
questions, so I must also accept that the best I can hope for is to make
your evasion clear to anyone who might come across this thread.
>> >> How can there be more? Is there a natural number that is not in the
>> >> potentially infinite set N?
>> >
>> > In set theory there must be more. There is no potential infinity.
>>
>> As you say, there is no potential infinity so what on Earth did you
>> think you were asking about set theory?
>
> Since all definable natnumbers are in FISONs, the actually infinite
> set (larger than all FISONs) must contain more than definable numbers.
Why are you so modest? You have discovered a universal truth that goes
far beyond definablility. It's equally true that all natnumbers that
are greater than or equal to 1 are in FISONs, so the actually infinite
set must contain more than numbers that are greater than or equal to 1.
And you can apply it to other sets as well. Consider the finite initial
subsets of the even numbers (FISENs). All even numbers are in FISENs,
so the actually infinite set of even numbers must contain more than even
numbers, despite it being the set from which the FISENs are drawn!
It's just a dishonest word game. Shame on you.
>> Mathematics (what you call set theory) proves statements like
>>
>> for every x ∈ N, lim_{n->oo} e_n(x) = 0.
>
> It also proves...
I need to jump in here. You know that this means you are agreeing that
e(x) = 0 is the limit function in mathematics as well as in WMaths, yes?
I hope you can see how well you hiding your true opinions. You suggest
further up that it's not the limit function (in "set theory"), and here
you seem to suggest it is!
<cut>
--
Ben.
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-14 05:49 -0700 |
| Message-ID | <78f9593a-8a35-42e4-aa6f-03feaba1be21@googlegroups.com> |
| In reply to | #210652 |
Am Samstag, 14. September 2019 03:15:30 UTC+2 schrieb Ben Bacarisse:
> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
>
> > Am Freitag, 13. September 2019 01:40:30 UTC+2 schrieb Ben Bacarisse:
> >> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>
> CONTEXT (why do you keep cutting key facts?): The e_n are a family of
> functions: e_n(x) = 1 if x >= n, 0 otherwise.
Yes, we had that already. They look like the following graph:
_________________----------------------------
We cannot repeat everything because the contributions get too long and will not be read by onlookers.
>
> >> >> lim_{n->oo} e_n(x) = 0.
> >> >
> >> > That is true for potential infinity (my book) and for every definable
> >> > n (there are infinitely many in set theory), followed by infinitely
> >> > many undefinable natnumbers.
> >>
> >> Oh! So in WMaths the limit function is e(x) = 0. I thought you denied
> >> this.
> >
> > Up to every definable n this is correct.
>
> You are being evasive! You cut the full quote. Why would you do that?.
We cannot repeat everything because the contribution get too long and will not be read by onlookers.
> You agreed that, in WMaths,
>
> for every x in N, lim_{n->oo} e_n(x) = 0
Yes, but every such x is not the last one. Therefore we can only say "up to every x the function is zero".
>
> and that is all the definition requires for e(x) = 0 to be the limit
> function. Yet you won't say "yes" without some added mysterious
> qualification.
>
> Of course, you can change your mind. You can retract your prior
> agreement that, in WMaths, lim_{n->oo} e_n(x) = 0 for every x in N, but
> you are not doing that either, it seems.
Look, the function f(x) = 1/x has limit 0. That is a firm, existing number or point.
But the limit function e(x) = 0 does not exist for all x because there are not all x in pot. inf. Therefore we can only say what I said above: up to every x or n.
> > It is easy: Since all definable natnumbers are in FISONs, the actually
> > infinite set (larger than all FISONs) must contain more than definable
> > numbers.
>
> More evasion.
A clear statement. Think better about it.
> Please confirm that you are claiming that, in what you
> call "set theory", e(x) = 0 is /not/ the point-wise limit of the
> function sequence I gave.
It is the limit for all definable numbers. But most numbers are undefinable.
According to set theory there are ℵo natnumbers. ℵo > cardinality of every FISON. Much larger.
>
> > Since all definable natnumbers are in FISONs, the actually infinite
> > set (larger than all FISONs) must contain more than definable numbers.
>
> Why are you so modest? You have discovered a universal truth that goes
> far beyond definablility. It's equally true that all natnumbers that
> are greater than or equal to 1 are in FISONs,
That is only true for definable natnumbers. For dark numbers we don't know anything but that they are undefinable.
> And you can apply it to other sets as well. Consider the finite initial
> subsets of the even numbers (FISENs). All even numbers are in FISENs,
All definable even numbers!
> I need to jump in here. You know that this means you are agreeing that
> e(x) = 0 is the limit function in mathematics as well as in WMaths, yes?
I told you above what that means.
This is the alternative with definition of endsegment E(n) = {n, n+1, n+2, ...}:
∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
But
∀n ∈ ℕ: E(1) ∩ E(2) ∩ E(3) ∩ ... ∩ E(n) ∩ ... ∩ <dark> = { } (**).
Since (*) contains already all natural numbers, the addition in (**) must be different from all natural numbers: <dark>.
Set theorists deny this. They claim that every endsegment E(n) is followed by infinitely many endsegments, but there are not infinitely many endsegmnets following upon every endsegment E(n). That means the intersection of those following endsegments <dark> which are producing the empty intersections in (**) is empty. That means they are not always there. That is what I'd call in German hirnrissig. Don't know whether hair-brained has sufficient power to translate it.
Regards, WM
Regards, WM
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-14 15:29 +0100 |
| Message-ID | <87zhj7gdcy.fsf@bsb.me.uk> |
| In reply to | #210665 |
Ganzhinterseher <claus.vonnesser@gmail.com> writes:
> Am Samstag, 14. September 2019 03:15:30 UTC+2 schrieb Ben Bacarisse:
>> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Hochschule Augsburg.)
>>
>> > Am Freitag, 13. September 2019 01:40:30 UTC+2 schrieb Ben Bacarisse:
>> >> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>>
>> CONTEXT (why do you keep cutting key facts?): The e_n are a family of
>> functions: e_n(x) = 1 if x >= n, 0 otherwise.
>
> Yes, we had that already. They look like the following graph:
>
> _________________----------------------------
>
> We cannot repeat everything because the contributions get too long and
> will not be read by onlookers.
Indeed, but that is one line defining a set of functions that are later
referenced. Study how I do it and you will see that I keep important
context without the posts getting too long. You cut material in order
to introduce changes as you need them. For example, your "up to"
introduced below and the dishonest change when you magically made my "E"
change from a set to a sequence. I need to keep the definitions visible
to prevent such trickery.
<cut>
>> You agreed that, in WMaths,
>>
>> for every x in N, lim_{n->oo} e_n(x) = 0
>
> Yes, but every such x is not the last one. Therefore we can only say
> "up to every x the function is zero".
Don't be silly. WMaths has sets like N x {0} and functions like e(x) =
0, and it can prove facts about every member of a set. Every x in N is
mapped to 0 by e(x) and every x in N has lim_{n->oo} e_n(x) = 0. e(x)
is the limit function.
>> and that is all the definition requires for e(x) = 0 to be the limit
>> function. Yet you won't say "yes" without some added mysterious
>> qualification.
>>
>> Of course, you can change your mind. You can retract your prior
>> agreement that, in WMaths, lim_{n->oo} e_n(x) = 0 for every x in N, but
>> you are not doing that either, it seems.
>
> Look, the function f(x) = 1/x has limit 0. That is a firm, existing number or point.
>
> But the limit function e(x) = 0 does not exist for all x because there
> are not all x in pot. inf.
>
> Therefore we can only say what I said above: up to every x or n.
That won't wash. If e(x) is not the limit function, then the examples
in your book are wrong too. If e(x) is the limit function you should
admit that it is. You simply won't settle the matter either way because
you can't. You don't want to admit you book does reflect your made-up
WMaths, but you don't want e(x) = 0 to be the limit of (e_n).
>> > It is easy: Since all definable natnumbers are in FISONs, the actually
>> > infinite set (larger than all FISONs) must contain more than definable
>> > numbers.
>>
>> More evasion.
>
> A clear statement. Think better about it.
I did not say it was not clear. I said it was evasive and it was:
clearly evasive. Why? Because I asked you (twice now) to confirm that
according to you the limit is not e(x) = 0 in "set theory". Instead of
"yes" or "no" you post the above evasive nonsense. Will you confirm (or
deny) that you do indeed think that e(x) = 0 is not the limit function
in "set theory" (AKA ordinary mathematics), or will post something else
that is a bot related but not a yes or a no?
>> Please confirm that you are claiming that, in what you
>> call "set theory", e(x) = 0 is /not/ the point-wise limit of the
>> function sequence I gave.
>
> It is the limit for all definable numbers. But most numbers are
> undefinable.
Again, an evasive answer. I think it means no, you do not think that
e(x) = 0 is the limit function in standard analysis. Note that I don't
care why you think it, I want the world to know that you deny it.
>> And you can apply it to other sets as well. Consider the finite initial
>> subsets of the even numbers (FISENs). All even numbers are in FISENs,
>
> All definable even numbers!
The editing here is so dishonest I won't reply. If anyone really does
read this, they need to look at the parent article to see what I said
rather, than what you have edited to suit your own ends.
>> I need to jump in here. You know that this means you are agreeing that
>> e(x) = 0 is the limit function in mathematics as well as in WMaths, yes?
>
> I told you above what that means.
And again, you cut the text of yours that shows I am right. Anyone who
cares can go and look at what I was responding to when I said "I need to
jump in here".
> This is the alternative with definition of endsegment E(n) = {n, n+1,
> n+2, ...}:
In the past you have even lied about what a trailing ... means. Why
don't you use closed forms like E(n) = { k | k ∈ N /\ k >= n } (to
borrow how you write this in your book)? I think I know why. You like
notation that shows sets are sequences, evolving and growing, not sets
that just are as a result of some property possessed by all elements.
> ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
This is true. In fact, ∩_{1<=k<=n} E(k) = E(n). The intersection of
them all is lim_{n->oo} E(n) = {}.
> But
>
> ∀n ∈ ℕ: E(1) ∩ E(2) ∩ E(3) ∩ ... ∩ E(n) ∩ ... ∩ <dark> = { } (**).
>
> Since (*) contains already all natural numbers, the addition in (**)
> must be different from all natural numbers: <dark>.
Silly. For one thing, the "for all n" is daft because the formula that
follows it does not depend on n, but more importantly, if
<dark> ∩ E(1) ∩ E(2) ∩ E(3) ∩ ... = {}
then
E(1) ∩ E(2) ∩ E(3) ∩ ... = {}
because <dark> contains (according to you) no numbers that are in any
E(k).
> Set theorists deny this.
Of course. It's a silly thing to write.
> They claim that every endsegment E(n) is followed by infinitely many
> endsegments, but there are not infinitely many endsegmnets following
> upon every endsegment E(n). That means the intersection of those
> following endsegments <dark> which are producing the empty
> intersections in (**) is empty. That means they are not always
> there. That is what I'd call in German hirnrissig. Don't know whether
> hair-brained has sufficient power to translate it.
I can't follow this waffle. Mathematicians claim that a number can only
be in the intersection of a family of subsets of N if it is in every one
of those subsets.
For anyone who cares, the trouble you have is that you can only think of
infinite things as processes evolving over time. The intersections here
are made (in your mind) by chipping away finite sets from an infinite
granite block of numbers. Mathematics, on the other hand, defines
things that are, complete, once and for all, with no reference to time
or action. You just prove that for any k, k ∉ E(k+1) to show that the
intersection is empty.
--
Ben.
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-14 08:38 -0700 |
| Message-ID | <e881c729-f9e1-487e-a815-b4d30ece13c7@googlegroups.com> |
| In reply to | #210666 |
Am Samstag, 14. September 2019 16:29:52 UTC+2 schrieb Ben Bacarisse:
> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
> > This is the alternative with definition of endsegment E(n) = {n, n+1,
> > n+2, ...}:
>
> In the past you have even lied about what a trailing ... means. Why
> don't you use closed forms like E(n) = { k | k ∈ N /\ k >= n }
I use both.
> (to
> borrow how you write this in your book)? I think I know why. You like
> notation that shows sets are sequences, evolving and growing, not sets
> that just are as a result of some property possessed by all elements.
Maybe.
>
> > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
>
> This is true. In fact, ∩_{1<=k<=n} E(k) = E(n). The intersection of
> them all is lim_{n->oo} E(n) = {}.
The intersection of them all is not the limit!
Understand that the terms of the sequence do not contain its limit.
>
> > But
> >
> > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ E(3) ∩ ... ∩ E(n) ∩ ... ∩ <dark> = { } (**).
> >
> > Since (*) contains already all natural numbers, the addition in (**)
> > must be different from all natural numbers: <dark>.
>
> Silly. For one thing, the "for all n" is daft because the formula that
> follows it does not depend on n,
That does not matter.
> Mathematicians claim that a number can only
> be in the intersection of a family of subsets of N if it is in every one
> of those subsets.
Mathematicians claim that an endsegment can only exists, if it is in (*).
> Mathematics, on the other hand, defines
> things that are, complete, once and for all, with no reference to time
> or action.
Then there are no further endsegments than those in (*). How would a larger set than all finite sets be possible?
REgards, WM
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 02:11 +0100 |
| Message-ID | <87lfuqfjnd.fsf@bsb.me.uk> |
| In reply to | #210667 |
Ganzhinterseher <claus.vonnesser@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)
> Am Samstag, 14. September 2019 16:29:52 UTC+2 schrieb Ben Bacarisse:
>> Ganzhinterseher <claus.vonnesser@gmail.com> writes:
>
>
>> > This is the alternative with definition of endsegment E(n) = {n, n+1,
>> > n+2, ...}:
>>
>> In the past you have even lied about what a trailing ... means. Why
>> don't you use closed forms like E(n) = { k | k ∈ N /\ k >= n }
>
> I use both.
>
>> (to
>> borrow how you write this in your book)? I think I know why. You like
>> notation that shows sets are sequences, evolving and growing, not sets
>> that just are as a result of some property possessed by all elements.
>
> Maybe.
>>
>> > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
>>
>> This is true. In fact, ∩_{1<=k<=n} E(k) = E(n). The intersection of
>> them all is lim_{n->oo} E(n) = {}.
>
> The intersection of them all is not the limit!
Your denial of this fact is duly noted.
> Understand that the terms of the sequence do not contain its limit.
Understood. This is not uncommon, and applies to WMaths set sequence
limits too. For example, in your book you correctly state that the
limit of the function sequence (f_n) with f_n(x) = x^n over [0, 1] is
the set
(0, 1] x {0} ∪ {(1, 1)}
The terms of this sequence do not contain its limit either.
Note how unequivocal your answer in the book is:
f(x) = 1 if x = 1, 0 otherwise
simply is the point-wise limit of (f_n). No hedging. You won't give
such an unequivocal answer about the limit of the (e_n) defined as
e_n(x) = 1 if x >= n, 0 otherwise
because you don't like the answer. (It's e(x) = 0.)
Nor, I notice, will you confirm that you deny that e(x) = 0 is the limit
function as defined by standard analysis. Again, you don't want it to
be, but you don't want a clear denial in the record, so you hedge.
>> > But
>> >
>> > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ E(3) ∩ ... ∩ E(n) ∩ ... ∩ <dark> = { } (**).
>> >
>> > Since (*) contains already all natural numbers, the addition in (**)
>> > must be different from all natural numbers: <dark>.
>>
>> Silly. For one thing, the "for all n" is daft because the formula that
>> follows it does not depend on n,
>
> That does not matter.
Sure, but it's helpful for people to see you write things like that.
Does your cutting of it mean you now agree with me that since <dark>
"must be different from all natural numbers", it can't have any effect
on the intersection of any number of end segments? I.e. do you agree
that (**) includes a term that can have no effect and can therefore be
omitted?
>> Mathematicians claim that a number can only
>> be in the intersection of a family of subsets of N if it is in every one
>> of those subsets.
>
> Mathematicians claim that an endsegment can only exists, if it is in
> (*).
No mathematician would even say that a set /could/ be in an equation.
Do you mean that every end segment is E(n) for some n in N? If not that
trivial statement, what?
>> Mathematics, on the other hand, defines
>> things that are, complete, once and for all, with no reference to time
>> or action.
>
> Then there are no further endsegments than those in (*). How would a
> larger set than all finite sets be possible?
By the axiom of infinity. All finite sets are strictly smaller than all
infinite sets.
You know this of course. You are probably just playing another one of
your word games with "all", but I don't know what the game is this time.
--
Ben.
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-11 15:11 -0700 |
| Message-ID | <ff5c0d2d-e89d-42ba-a18c-45f11400dc68@googlegroups.com> |
| In reply to | #210427 |
On Tuesday, September 10, 2019 at 9:25:38 PM UTC-4, Ben Bacarisse wrote: > Here's what is actually meant by the point-wise limit: > > Let DON'T do it! MAKE HIM do it! HE CAN'T. THAT'S THE POINT. HE'S *TOO*STUPID*.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 02:23 +0100 |
| Message-ID | <87sgp2jojh.fsf@bsb.me.uk> |
| In reply to | #210484 |
George Greene <greeneg@email.unc.edu> writes: > On Tuesday, September 10, 2019 at 9:25:38 PM UTC-4, Ben Bacarisse wrote: >> Here's what is actually meant by the point-wise limit: >> >> Let > > DON'T do it! > MAKE HIM do it! > HE CAN'T. THAT'S THE POINT. > HE'S *TOO*STUPID*. <sigh>. You've not been following! What I quoted is the definition from the textbook that Dr. Wolfgang Mückenheim (or Mueckenheim) wrote. He knows it is, and he approved the translation when this last came up. At that time, he denied that my (e_n) had a limit function at all. Now, apparently, it has a limit, but not exactly e(x) = 0. That his students might find this flailing about is the best I can hope for. -- Ben.
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| From | jvr <jrennenkampff@googlemail.com> |
|---|---|
| Date | 2019-09-12 02:08 -0700 |
| Message-ID | <4b6d7c52-d41b-4a58-afc2-d492fa5af5e2@googlegroups.com> |
| In reply to | #210507 |
On Thursday, September 12, 2019 at 3:23:15 AM UTC+2, Ben Bacarisse wrote: > George Greene <greeneg@email.unc.edu> writes: > > > On Tuesday, September 10, 2019 at 9:25:38 PM UTC-4, Ben Bacarisse wrote: > >> Here's what is actually meant by the point-wise limit: > >> > >> Let > > > > DON'T do it! > > MAKE HIM do it! > > HE CAN'T. THAT'S THE POINT. > > HE'S *TOO*STUPID*. > > <sigh>. You've not been following! What I quoted is the definition > from the textbook that Dr. Wolfgang Mückenheim (or Mueckenheim) wrote. > He knows it is, and he approved the translation when this last came up. > At that time, he denied that my (e_n) had a limit function at all. Now, > apparently, it has a limit, but not exactly e(x) = 0. That his students > might find this flailing about is the best I can hope for. > > -- > Ben. The man is a charlatan. It is a mistake to take him seriously.
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-11 15:10 -0700 |
| Message-ID | <ccc25de3-ad57-4f8f-ad4c-ffe1065f725c@googlegroups.com> |
| In reply to | #210346 |
On Monday, September 9, 2019 at 4:21:25 PM UTC-4, Ganzhinterseher wrote: > Let's apply it to this problem: How many > natnumbers can we remove from 1, 2, 3, ... without emptying this set? DAMN, you're stupid. You may have noticed that mathematicians use formal rather than natural language for a reason. ANY AND EVERY *individual* natural number can be so removed. The fact that saying you can therefore remove "all" of them would look like a contradiction PROVES YOU'RE STUPID for even PHRASING the question this way. You are not asking an actual question.
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-12 07:29 -0700 |
| Message-ID | <103130b4-3429-4316-936e-be70fd31a96a@googlegroups.com> |
| In reply to | #210483 |
Am Donnerstag, 12. September 2019 00:10:04 UTC+2 schrieb George Greene:
> On Monday, September 9, 2019 at 4:21:25 PM UTC-4, Ganzhinterseher wrote:
> > Let's apply it to this problem: How many
> > natnumbers can we remove from 1, 2, 3, ... without emptying this set?
>
> ANY AND EVERY *individual* natural number can be so removed.
But always infinitely many will remain.
> You are not asking an actual question.
I am asking this question:
Define for given k: {E(1),E(2), E(3), ...}\{E(2),..., E(k)} and take the intersection of the result: ∩{E(1), E(k+1),E(k+2), E(k+3),...}
Can you define a k for which the intersection is not empty? No. Therefore there are always infinitely many endsegments remaining. You may boast or "prove" that you can define them, but you cannot.
Regards, WM
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| From | Transfinite Numbers <bursejan@gmail.com> |
|---|---|
| Date | 2019-09-11 14:00 -0700 |
| Message-ID | <ef80bb23-0039-4e02-8022-99fcb48b5405@googlegroups.com> |
| In reply to | #210293 |
Q: Can the empty set be the limit of a sequence of non-empty sets? A: Yes On Sunday, September 8, 2019 at 6:49:47 PM UTC+2, Ganzhinterseher wrote: > Sets and their elements are the crown jewels of set theory. Therefore a great damage results from uncontrolled loss. The terms of a sequence of sets can change in their elements and their cardinality in a controlled way, defined by a formula. But if a sequence of sets has exclusively non-empty elements, then the limit cannot be empty because there is no controlled change or exchange possible between all terms and the limit. > > Why do nevertheless many mathematicians believe in this confusion? That is a psychological problem. Mathematics is not involved. For more information see https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 341. > > Regards, WM
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