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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 3 of 13 — ← Prev page 1 2 [3] 4 5 … 13 Next page →
| From | Exfalso Quodlibet <exflaso.quodlibet@gmail.com> |
|---|---|
| Date | 2019-09-14 12:13 -0700 |
| Message-ID | <f1c5c682-1090-48f9-a8d4-8040b44a5bf7@googlegroups.com> |
| In reply to | #210598 |
On Friday, September 13, 2019 at 7:13:55 AM UTC-4, Ganzhinterseher wrote:
> Am Donnerstag, 12. September 2019 23:27:43 UTC+2 schrieb Exfalso Quodlibet:
> > On Thursday, September 12, 2019 at 4:19:58 PM UTC-4, Ganzhinterseher wrote:
>
>
> > > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
> >
> > And yet ∩E(n) = { }!
>
> For all definable natnumbers (*) holds.
It's trivial, so it's silly that you keep repeating it as if it's some mystical secret.
For any natural number n, ∩_{1≤k≤n} E(k) is obviously E(n), which contains infinitely many elements: E(n) = {k in N | k > n}.
> > If you analyze the sequence {1/n}, you'd find that "the state" is always positive, and yet the limit is not. Astounding!
>
> No, it's not. The terms of the sequence approximate 0
And every term is positive. 0 is not positive. Thus, the properties of "the state" are not guaranteed to carry over to the limit, and so on for every other point I made. So, as I said:
> > Pretty much no property of "the state" is guaranteed to carry over to the limit, so your blind insistence on only looking at "the state" is misguided.
>
> There are dark numbers.
Rubbish.
EFQ
[toc] | [prev] | [next] | [standalone]
| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-15 03:00 -0700 |
| Message-ID | <f453b5a9-5625-45f5-89d8-ff8141b353f9@googlegroups.com> |
| In reply to | #210681 |
Am Samstag, 14. September 2019 21:13:16 UTC+2 schrieb Exfalso Quodlibet:
> On Friday, September 13, 2019 at 7:13:55 AM UTC-4, Ganzhinterseher wrote:
> > Am Donnerstag, 12. September 2019 23:27:43 UTC+2 schrieb Exfalso Quodlibet:
> > > On Thursday, September 12, 2019 at 4:19:58 PM UTC-4, Ganzhinterseher wrote:
> >
> >
> > > > ∀n ∈ ℕ: E(1) ∩ E(2) ∩ ... ∩ E(n) =/= { } (*)
> > >
> > > And yet ∩E(n) = { }!
> >
> > For all definable natnumbers (*) holds.
>
> It's trivial, so it's silly that you keep repeating it as if it's some mystical secret.
It is trivial that there are not more definable natnumbers then appearing in (*). Therfeore for all of them we have ∩E(n) =/= { }.
>
> For any natural number n, ∩_{1≤k≤n} E(k) is obviously E(n), which contains infinitely many elements: E(n) = {k in N | k > n}.
Other definable numbers are not available.
>
> > > If you analyze the sequence {1/n}, you'd find that "the state" is always positive, and yet the limit is not. Astounding!
> >
> > No, it's not. The terms of the sequence approximate 0
>
> And every term is positive. 0 is not positive. Thus, the properties of "the state" are not guaranteed to carry over to the limit, and so on for every other point I made.
But ∩E(n) is not the limit but only the intersection over all terms of the sequence.
>So, as I said:
>
> > > Pretty much no property of "the state" is guaranteed to carry over to the limit, so your blind insistence on only looking at "the state" is misguided.
> >
> > There are dark numbers.
>
> Rubbish.
>
Agreed. But this implies that set theory is rubbish.
Regards, WM
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| From | jvr <jrennenkampff@googlemail.com> |
|---|---|
| Date | 2019-09-15 03:38 -0700 |
| Message-ID | <6b080ec0-676f-4905-b557-d229e1160a4b@googlegroups.com> |
| In reply to | #210747 |
[...]
>
> But ∩E(n) is not the limit but only the intersection over all terms of the sequence.
This is an obvious error. I know it's impossible to convince you, but have you considered that
E(n) = ∪_{k>=n} E(k)?
Which makes ∩E(n) = lim sup E(n).
And what do you think, praytell, that lim inf E(n) might be?
And do you need help showing that these are equal?
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-15 05:42 -0700 |
| Message-ID | <e94603f4-866c-45cc-a748-a6245054487e@googlegroups.com> |
| In reply to | #210748 |
Am Sonntag, 15. September 2019 12:38:59 UTC+2 schrieb jvr:
> [...]
> >
> > But ∩E(n) is not the limit but only the intersection over all terms of the sequence.
>
> This is an obvious error. I know it's impossible to convince you,
It is impoosible to convince me that the bijection of |N ans |Q can be proved in the limit. There must be clear facts. Every n and every q must have their partner element.
> but have you considered that
>
> E(n) = ∪_{k>=n} E(k)?
>
> Which makes ∩E(n) = lim sup E(n).
>
> And what do you think, praytell, that lim inf E(n) might be?
Unfortunately set theorists usually are confused or like to be confusing.
Limits as defined on p. 55 of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf are not sufficient to prove bijections or the diagonal argument. There we need facts, element by element, for all elements, none missing.!
The simplest way to understand the difference is the sequence of partial sums of the series 1/2^n:
∀n ∈ ℕ: 1/2 + 1/4 + ... + 1/2^n < 1 .
Can you see universal quantification? There is no term of the sequence completeing the limit 1.
That concerns all natural numbers n and implies
SUM 1/2^n < 1
n ∈ ℕ
differing from the limit
SUM 1/2^n < 1 .
n → ∞
Regards, WM
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| From | jvr <jrennenkampff@googlemail.com> |
|---|---|
| Date | 2019-09-15 06:02 -0700 |
| Message-ID | <dc19d47e-5ab7-4525-80f3-a1afc150c7c9@googlegroups.com> |
| In reply to | #210758 |
On Sunday, September 15, 2019 at 2:42:32 PM UTC+2, Ganzhinterseher wrote:
> Am Sonntag, 15. September 2019 12:38:59 UTC+2 schrieb jvr:
> > [...]
> > >
> > > But ∩E(n) is not the limit but only the intersection over all terms of the sequence.
> >
> > This is an obvious error. I know it's impossible to convince you,
>
> It is impoosible to convince me that the bijection of |N ans |Q can be proved in the limit. There must be clear facts. Every n and every q must have their partner element.
>
> > but have you considered that
> >
> > E(n) = ∪_{k>=n} E(k)?
> >
> > Which makes ∩E(n) = lim sup E(n).
> >
> > And what do you think, praytell, that lim inf E(n) might be?
>
> Unfortunately set theorists usually are confused or like to be confusing.
>
> Limits as defined on p. 55 of https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf are not sufficient to prove bijections or the diagonal argument. There we need facts, element by element, for all elements, none missing.!
>
> The simplest way to understand the difference is the sequence of partial sums of the series 1/2^n:
>
> ∀n ∈ ℕ: 1/2 + 1/4 + ... + 1/2^n < 1 .
>
> Can you see universal quantification? There is no term of the sequence completeing the limit 1.
>
> That concerns all natural numbers n and implies
>
> SUM 1/2^n < 1
> n ∈ ℕ
>
> differing from the limit
>
> SUM 1/2^n < 1 .
> n → ∞
>
> Regards, WM
Mücke, this is too blatent, even for you. The point I made, which is
irrefutable, was that
" But ∩E(n) is not the limit but only the intersection over all terms of the sequence."
is an obvious error - so you blithely ignore it. That's probably known as a
proof in muckmeatics.
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-15 13:31 -0700 |
| Message-ID | <8ca2f284-8ef1-4e6b-9e5e-9bd46eed1e71@googlegroups.com> |
| In reply to | #210761 |
Am Sonntag, 15. September 2019 15:03:01 UTC+2 schrieb jvr: > The point I made, which is > irrefutable, was that > > " But ∩E(n) is not the limit but only the intersection over all terms of the sequence." > > is an obvious error You are wrong. I told you why. If you cannot understand, I cannot help you. Regards, WM
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-15 07:54 -0700 |
| Message-ID | <e215a68a-38ba-4db1-a89a-67537bf975c7@googlegroups.com> |
| In reply to | #210758 |
On Sunday, September 15, 2019 at 8:42:32 AM UTC-4, Ganzhinterseher wrote: > Unfortunately set theorists usually are confused or like to be confusing. The fact THAT YOU are confused does NOT mean that ANYthing is confusing!! > > Limits as defined on p. 55 YOU DO *NOT*GET* to "define limits"! "Limit" IS ALREADY IN the dictionary!! "Limit of a sequence of sets" is not, really, but there is certainly NO reason why anyone should defer to YOUR definition!!
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-15 07:27 -0700 |
| Message-ID | <9d12e3f6-c4dd-4d13-8991-1cd2553942f8@googlegroups.com> |
| In reply to | #210748 |
On Sunday, September 15, 2019 at 6:38:59 AM UTC-4, jvr wrote:
> I know it's impossible to convince you, but have you considered that
>
> E(n) = ∪_{k>=n} E(k)?
>
> Which makes ∩E(n) = lim sup E(n).
Why are you using lim sup when he's talking about NATURAL numbers???
lim sup involves limit points and infinite accumulation, and sets
of points THAT ARE REALS, or something.
It is NOT even DEFINED in the context of endsegments-of-N!!
I TOLD YOU to ask HIM to define "limit of a set"!
In case you hadn't noticed, THAT TERM IS *NON*-SENSICAL!
THERE IS NO SUCH CONCEPT!!
[toc] | [prev] | [next] | [standalone]
| From | jvr <jrennenkampff@googlemail.com> |
|---|---|
| Date | 2019-09-15 09:37 -0700 |
| Message-ID | <32cb5cf0-cde2-4af4-bc71-965814e19337@googlegroups.com> |
| In reply to | #210764 |
On Sunday, September 15, 2019 at 4:28:00 PM UTC+2, George Greene wrote:
> On Sunday, September 15, 2019 at 6:38:59 AM UTC-4, jvr wrote:
> > I know it's impossible to convince you, but have you considered that
> >
> > E(n) = ∪_{k>=n} E(k)?
> >
> > Which makes ∩E(n) = lim sup E(n).
>
> Why are you using lim sup when he's talking about NATURAL numbers???
E(n) is a sequence of sets.
> lim sup involves limit points and infinite accumulation, and sets
> of points THAT ARE REALS, or something.
> It is NOT even DEFINED in the context of endsegments-of-N!!
For sequences of sets there is a "usual" definition of lim, limsup and liminf. Other definitions are possible, corresponding e.g. to other
topologies for the set of indicator functions.
>
>
> I TOLD YOU
Really? You think it makes sense to TELL PEOPLE TO DO this or that? Even
if I had been aware of your command, I am not obliged to follow it, am I?
> to ask HIM to define "limit of a set"!
> In case you hadn't noticed, THAT TERM IS *NON*-SENSICAL!
> THERE IS NO SUCH CONCEPT!!
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-15 07:26 -0700 |
| Message-ID | <821d965f-168b-4371-bca0-d178bb2be998@googlegroups.com> |
| In reply to | #210747 |
On Sunday, September 15, 2019 at 6:00:42 AM UTC-4, Ganzhinterseher wrote:
> It is trivial that there are not more definable natnumbers
It is trivial that using the phrase "definable natnumbers" proves you
are an ignorant dipshit. EVERY natural number IS TRIVIALLY definable.
It's not like there could be some DOUBT about one. It's NOT like there
COULD POSSIBLY exist some "un"definable natural number. The "definable"
in "definable natural number" IS REDUNDANT and when you SAY "definable
natural number", you PROVE YOU DIDN'T KNOW THAT, which means you do NOT
get to pontificate about any of this stuff!
> then appearing in (*).
> Therfeore for all of them we have ∩E(n) =/= { }.
OF COURSE we do, but the intersection OF ALL of them IS NOT ∩E(n) for ANY n,
no matter how big n may get.
All the ∩E(n) ARE FINITE intersections, but the intersection OF ALL
the E(n) IS DIFFERENT FROM ALL the various ∩E(n) because IT is the intersection
OF INFINITELY many sets.
How you could CONTINUE to KEEP EQUIVOCATING on "All" AFTER THIRTY
YEARS is FAR beyond the pale of rationality.
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| From | Ganzhinterseher <claus.vonnesser@gmail.com> |
|---|---|
| Date | 2019-09-16 10:33 -0700 |
| Message-ID | <feaa9e60-65d7-4bfe-a74d-4f129c8b91e2@googlegroups.com> |
| In reply to | #210763 |
Am Sonntag, 15. September 2019 16:26:23 UTC+2 schrieb George Greene: > On Sunday, September 15, 2019 at 6:00:42 AM UTC-4, Ganzhinterseher wrote: > > It is trivial that there are not more definable natnumbers > > EVERY natural number IS TRIVIALLY definable. No. See below. > All the ∩E(n) ARE FINITE intersections, but the intersection OF ALL > the E(n) IS DIFFERENT FROM ALL the various ∩E(n) because IT is the intersection > OF INFINITELY many sets. First show where you get more definable endsegments than are in all the finite sets intersected in (*). Note that an infinite set must have more endsegments than all finite sets. Regards, WM
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-15 07:52 -0700 |
| Message-ID | <04826b36-a3d9-440c-8e8b-e1718fc6c4f0@googlegroups.com> |
| In reply to | #210747 |
On Sunday, September 15, 2019 at 6:00:42 AM UTC-4, Ganzhinterseher wrote: > But ∩E(n) is not the limit but only > the intersection over all terms of the sequence. That's abuse of notation, but if that's really what you mean by that notation (most people would say instead that ∩E(n) was dependent on the value of n and was either the intersection of all the endsegments up to the nth, or the intersection of all of them from the nth onward), then, yes, that intersection is empty. NOW, define what MIGHT be THE LIMIT of the sequence of E(n)'s. I repeat, ZFC does NOT ACTUALY EVEN HAVE ANY CONCEPT of "the limit of" sets. It DOES have a concept of LIMIT ORDINAL which could serve as a template/foundation FOR OTHER KINDS OF limits, but NONE of that is official.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-15 16:13 +0100 |
| Message-ID | <qllkev$o5u$1@news.albasani.net> |
| In reply to | #210765 |
On 15/09/2019 15:52, George Greene wrote:
> On Sunday, September 15, 2019 at 6:00:42 AM UTC-4, Ganzhinterseher wrote:
>> But ∩E(n) is not the limit but only
>> the intersection over all terms of the sequence.
>
> That's abuse of notation, but if that's really what you mean by that notation
> (most people would say instead that ∩E(n) was dependent on the value of n
> and was either the intersection of all the endsegments up to the nth, or the intersection of all of them from the nth onward), then, yes, that intersection
> is empty. NOW, define what MIGHT be THE LIMIT of the sequence of E(n)'s.
>
> I repeat, ZFC does NOT ACTUALY EVEN HAVE ANY CONCEPT of "the limit of" sets.
If S_n is a countable sequence of sets then limsup S_n and liminf S_n
have obvious definitions. How about saying that lim S_n exists if
limsup S_n and liminf S_n are equal, and (in that case) is equal to them?
limsup S_n = bigintersection_{n=1}^infty bigunion_{m=n}^infty S_m
liminf S_n = bigunion_{n=1}^infty bigintersection_{m=n}^infty S_m
> It DOES have a concept of LIMIT ORDINAL which could serve as a template/foundation FOR OTHER KINDS OF limits, but NONE of that is official.
>
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-15 21:29 +0100 |
| Message-ID | <qlm703$gmn$1@news.albasani.net> |
| In reply to | #210767 |
On 15/09/2019 16:13, Fred wrote:
> On 15/09/2019 15:52, George Greene wrote:
>> On Sunday, September 15, 2019 at 6:00:42 AM UTC-4, Ganzhinterseher wrote:
>>> But ∩E(n) is not the limit but only
>>> the intersection over all terms of the sequence.
>>
>> That's abuse of notation, but if that's really what you mean by that
>> notation
>> (most people would say instead that ∩E(n) was dependent on the value of n
>> and was either the intersection of all the endsegments up to the nth,
>> or the intersection of all of them from the nth onward), then, yes,
>> that intersection
>> is empty. NOW, define what MIGHT be THE LIMIT of the sequence of E(n)'s.
>>
>> I repeat, ZFC does NOT ACTUALY EVEN HAVE ANY CONCEPT of "the limit of"
>> sets.
>
> If S_n is a countable sequence of sets then limsup S_n and liminf S_n
> have obvious definitions. How about saying that lim S_n exists if
> limsup S_n and liminf S_n are equal, and (in that case) is equal to them?
>
> limsup S_n = bigintersection_{n=1}^infty bigunion_{m=n}^infty S_m
>
> liminf S_n = bigunion_{n=1}^infty bigintersection_{m=n}^infty S_m
A modicum of firtling around shows that is _the_ definition of the limit
of sets. Why do you think ZFC has no such concept?
>> It DOES have a concept of LIMIT ORDINAL which could serve as a
>> template/foundation FOR OTHER KINDS OF limits, but NONE of that is
>> official.
>>
>
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| From | George Greene <greeneg@email.unc.edu> |
|---|---|
| Date | 2019-09-15 16:55 -0700 |
| Message-ID | <fd35b293-dbf6-407e-ba20-5aa7fd709a19@googlegroups.com> |
| In reply to | #210767 |
On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote: > If S_n is a countable sequence of sets then limsup S_n and liminf S_n > have obvious definitions. They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!! > How about saying IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed, it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y* would ALREADY KNOW that this was THE USUAL definition of this term! THEY DON'T because IT ISN'T and IT DOESN'T! Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences OF POINTS (or sets of points), NOT about sequences of *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the sets (or of the sequences) have to belong to some OTHER realm, OTHER than sets, LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!! SETS IN GENERAL do NOT have ORDER!!!
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 12:59 +0100 |
| Message-ID | <qlnter$7a9$1@news.albasani.net> |
| In reply to | #210777 |
On 16/09/2019 00:55, George Greene wrote: > On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote: > >> If S_n is a countable sequence of sets then limsup S_n and liminf S_n >> have obvious definitions. > > They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!! > >> How about saying > > IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed, > it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y* > would ALREADY KNOW that this was THE USUAL definition of this term! > THEY DON'T > because IT ISN'T > and IT DOESN'T! > > Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences > OF POINTS (or sets of points), NOT about sequences of > *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the sets > (or of the sequences) have to belong to some OTHER realm, OTHER than sets, > LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!! > SETS IN GENERAL > do NOT have ORDER!!! > Do calm down! Is seems that jvr agrees with what I wrote. It seems that where sequences of sets are concerned lim =df limsup = liminf, so long as limsup and liminf both exist and are equal.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 13:12 +0100 |
| Message-ID | <qlnu72$459$1@news.albasani.net> |
| In reply to | #210777 |
On 16/09/2019 00:55, George Greene wrote: > On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote: > >> If S_n is a countable sequence of sets then limsup S_n and liminf S_n >> have obvious definitions. > > They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!! I guessed at the definitions (the guesses came to mind immediately, hence the "obvious") and they turned out to be correct. >> How about saying > > IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed, > it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y* It is generally known to set theorists, which is all that matters. > would ALREADY KNOW that this was THE USUAL definition of this term! Hardly. Certainly not literally everybody, and not even everybody contributing to this newsgroups which, you can hardly fail to have noticed, attracts a few idiots. > THEY DON'T > because IT ISN'T > and IT DOESN'T! > > Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences > OF POINTS (or sets of points), NOT about sequences of > *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the sets > (or of the sequences) have to belong to some OTHER realm, OTHER than sets, > LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!! > SETS IN GENERAL > do NOT have ORDER!!! What we need is someone like Rupert, who is familiar with set theory, to tell us if the lim = limsup = liminf definition is standard. If he says no I shall withdraw my claim.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 15:34 +0100 |
| Message-ID | <qlo6hs$kd9$1@news.albasani.net> |
| In reply to | #210787 |
On 16/09/2019 13:12, Fred wrote: > On 16/09/2019 00:55, George Greene wrote: >> On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote: >> >>> If S_n is a countable sequence of sets then limsup S_n and liminf S_n >>> have obvious definitions. >> >> They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!! > > I guessed at the definitions (the guesses came to mind immediately, > hence the "obvious") and they turned out to be correct. > >>> How about saying >> >> IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed, >> it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y* > > It is generally known to set theorists, which is all that matters. > >> would ALREADY KNOW that this was THE USUAL definition of this term! > > Hardly. Certainly not literally everybody, and not even everybody > contributing to this newsgroups which, you can hardly fail to have > noticed, attracts a few idiots. > >> THEY DON'T >> because IT ISN'T >> and IT DOESN'T! >> >> Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences >> OF POINTS (or sets of points), NOT about sequences of >> *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the >> sets >> (or of the sequences) have to belong to some OTHER realm, OTHER than >> sets, >> LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!! >> SETS IN GENERAL >> do NOT have ORDER!!! > > What we need is someone like Rupert, who is familiar with set theory, to > tell us if the lim = limsup = liminf definition is standard. If he says > no I shall withdraw my claim. The definition I gave appears on page 4 of volume I of Kuratowski's /Topology/, Academic Press, 1966. He write Limes for my lim, Lim inf for my liminf, and Lim sup for my limsup. I rest my case.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-16 23:49 +0100 |
| Message-ID | <877e67dfg4.fsf@bsb.me.uk> |
| In reply to | #210790 |
Fred <Fred@nowhere.invalid> writes: > On 16/09/2019 13:12, Fred wrote: >> On 16/09/2019 00:55, George Greene wrote: >>> On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote: >>> >>>> If S_n is a countable sequence of sets then limsup S_n and liminf S_n >>>> have obvious definitions. >>> >>> They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!! >> >> I guessed at the definitions (the guesses came to mind immediately, hence the "obvious") and they turned out to be correct. >> >>>> How about saying >>> >>> IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed, >>> it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y* >> >> It is generally known to set theorists, which is all that matters. >> >>> would ALREADY KNOW that this was THE USUAL definition of this term! >> >> Hardly. Certainly not literally everybody, and not even everybody contributing to this newsgroups which, you can hardly fail to have noticed, attracts a few idiots. >> >>> THEY DON'T >>> because IT ISN'T >>> and IT DOESN'T! >>> >>> Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences >>> OF POINTS (or sets of points), NOT about sequences of >>> *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the sets >>> (or of the sequences) have to belong to some OTHER realm, OTHER than sets, >>> LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!! >>> SETS IN GENERAL >>> do NOT have ORDER!!! >> >> What we need is someone like Rupert, who is familiar with set theory, >> to tell us if the lim = limsup = liminf definition is standard. If >> he says no I shall withdraw my claim. > > The definition I gave appears on page 4 of volume I of Kuratowski's > /Topology/, Academic Press, 1966. He write Limes for my lim, Lim inf > for my liminf, and Lim sup for my limsup. I rest my case. Essentially the same definition (though given rather informally) can be found early on in Hausdorff's "Mengenlehre" (1937). I relied on a 1957 English the translation where it's called "Set Theory". -- Ben.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-17 08:53 +0100 |
| Message-ID | <qlq3da$vre$1@news.albasani.net> |
| In reply to | #210851 |
On 16/09/2019 23:49, Ben Bacarisse wrote:
> Fred <Fred@nowhere.invalid> writes:
>
>> On 16/09/2019 13:12, Fred wrote:
>>> On 16/09/2019 00:55, George Greene wrote:
>>>> On Sunday, September 15, 2019 at 11:13:37 AM UTC-4, Fred wrote:
>>>>
>>>>> If S_n is a countable sequence of sets then limsup S_n and liminf S_n
>>>>> have obvious definitions.
>>>>
>>>> They are NOT obvious TO YOU, you LYING F#tard! GOOD GRIEF!!
>>>
>>> I guessed at the definitions (the guesses came to mind immediately, hence the "obvious") and they turned out to be correct.
>>>
>>>>> How about saying
>>>>
>>>> IT DOESN'T *F#*in'* MATTER what *YOU* say here!! IF this concept existed,
>>>> it WOULD ALREADY BE GENERALLY KNOWN to exist!! *E*V*E*R*Y*B*O*D*Y*
>>>
>>> It is generally known to set theorists, which is all that matters.
>>>
>>>> would ALREADY KNOW that this was THE USUAL definition of this term!
>>>
>>> Hardly. Certainly not literally everybody, and not even everybody contributing to this newsgroups which, you can hardly fail to have noticed, attracts a few idiots.
>>>
>>>> THEY DON'T
>>>> because IT ISN'T
>>>> and IT DOESN'T!
>>>>
>>>> Lim sup AS TRADITIONALLY/RATIONALLY/NORMALLY defined is about sequences
>>>> OF POINTS (or sets of points), NOT about sequences of
>>>> *S*E*T*S*!!! IN ORDER for these things to exist, the ELEMENTS of the sets
>>>> (or of the sequences) have to belong to some OTHER realm, OTHER than sets,
>>>> LIKE *REAL*NUMBERS*, that have notions OF ORDER AND DISTANCE!!
>>>> SETS IN GENERAL
>>>> do NOT have ORDER!!!
>>>
>>> What we need is someone like Rupert, who is familiar with set theory,
>>> to tell us if the lim = limsup = liminf definition is standard. If
>>> he says no I shall withdraw my claim.
>>
>> The definition I gave appears on page 4 of volume I of Kuratowski's
>> /Topology/, Academic Press, 1966. He write Limes for my lim, Lim inf
>> for my liminf, and Lim sup for my limsup. I rest my case.
>
> Essentially the same definition (though given rather informally) can be
> found early on in Hausdorff's "Mengenlehre" (1937). I relied on a 1957
> English the translation where it's called "Set Theory".
>
Thank you.
I've also found it in Kuratowski's /Introduction to set theory and
topology/, a wholly elementary text. Kuratowski has 'Lim' for 'Limes'
in his other book. An exercise (7 on p.61) asks the reader to show
that, with A a set and
( 1 if x in A
f_A(x) = (
( 0 if x in A^c (A's complement)
F = Lim F_n iff f_F = lim f_{F_n}(x)
where F_n is a sequence of sets and lim is the usual numerical limit.
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