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Groups > sci.logic > #210463 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-09-11 12:05 -0500 |
| Last post | 2019-09-11 23:15 -0500 |
| Articles | 20 on this page of 322 — 13 participants |
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Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:05 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Fred <Fred@nowhere.invalid> - 2019-09-11 18:37 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 18:32 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 01:15 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 19:30 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) temakoutera62@gmail.com - 2019-09-11 17:32 -0700
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 01:38 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 01:49 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) George Greene <greeneg@email.unc.edu> - 2019-09-14 18:22 -0700
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-15 02:32 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:19 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 03:29 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:41 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:19 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 22:46 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 13:02 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 10:26 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 00:21 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 18:24 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 02:10 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 20:41 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 03:34 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 22:43 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-16 23:12 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:27 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:26 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-17 11:53 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:55 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 22:19 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 21:23 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 22:31 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 22:04 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 23:21 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 22:40 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 00:27 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 23:55 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 00:59 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 00:12 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 10:15 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 09:35 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 11:00 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 10:14 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 11:26 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 10:42 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 13:10 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 12:36 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 13:49 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 12:59 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 14:12 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 20:25 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 13:30 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 14:45 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 14:14 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 15:29 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 14:38 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 15:56 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 20:38 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-18 22:03 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) André G. Isaak <agisaak@gm.invalid> - 2019-09-18 21:33 -0600
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 16:35 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:35 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 16:46 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 11:42 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 17:58 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 12:43 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 19:34 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 19:42 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 18:16 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 18:12 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:24 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 16:39 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 18:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 20:41 -0700
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 05:15 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-17 23:32 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 23:21 -0600
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 18:42 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-18 12:58 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 19:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 01:42 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-18 20:46 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-19 02:52 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 22:24 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 17:13 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 01:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 19:49 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 02:34 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 20:54 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 03:32 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-20 14:16 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-20 17:49 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-20 07:16 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 21:37 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-20 15:53 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-21 00:10 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 09:45 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-21 17:20 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Jim Burns <james.g.burns@att.net> - 2019-09-21 14:39 -0400
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-22 13:32 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-23 19:50 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-24 02:27 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-24 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 18:02 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:10 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:06 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:54 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-15 12:06 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 01:42 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 20:03 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:50 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 20:59 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 04:07 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 22:16 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 04:20 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 22:22 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 16:33 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 11:14 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-13 02:00 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-12 21:39 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben Fred <Fred@nowhere.invalid> - 2019-09-13 16:38 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-13 11:48 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben Fred <Fred@nowhere.invalid> - 2019-09-13 17:54 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 00:51 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 17:23 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 13:09 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 19:28 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 19:33 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 14:27 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 20:30 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 14:41 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 13:02 -0700
Re: Cantor was wrong about cardinality --- APOLOGY André G. Isaak <agisaak@gm.invalid> - 2019-09-14 14:08 -0600
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 21:18 +0100
Re: Cantor was wrong about cardinality --- APOLOGY André G. Isaak <agisaak@gm.invalid> - 2019-09-14 14:25 -0600
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:03 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:19 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 15:45 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 21:55 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:06 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:20 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 00:54 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 14:07 -0700
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 21:14 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:01 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:17 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 00:47 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 19:24 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-15 02:20 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:43 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-14 21:33 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:09 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-14 22:40 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:40 -0600
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-15 12:05 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 12:33 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 10:17 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:26 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 10:36 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 16:50 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 16:55 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 10:06 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:22 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 10:38 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:59 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 11:10 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 13:27 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 12:34 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 14:19 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 20:28 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 13:35 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 14:51 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 21:02 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 14:15 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 16:18 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 16:00 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 15:29 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 18:14 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Jeff Barnett <jbb@notatt.com> - 2019-09-16 23:34 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:16 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 14:25 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 16:21 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 16:01 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:21 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 15:46 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 18:07 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Me <invalid@invalid.de> - 2019-09-17 01:09 +0200
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 02:33 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 20:53 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:55 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 19:21 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:40 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 21:38 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 00:24 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 11:39 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Fred <Fred@nowhere.invalid> - 2019-09-17 17:55 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:38 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 13:17 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Keith Thompson <kst-u@mib.org> - 2019-09-17 11:13 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 13:29 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:36 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) peteolcott <Here@Home> - 2019-09-17 11:20 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) Fred <Fred@nowhere.invalid> - 2019-09-17 17:31 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 10:56 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (Concurrence) André G. Isaak <agisaak@gm.invalid> - 2019-09-17 11:29 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:32 +0100
Re: Cantor was wrong about cardinality --- (Correction) peteolcott <Here@Home> - 2019-09-17 12:49 -0500
Re: Cantor was wrong about cardinality --- (Correction) Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 19:59 +0100
Re: Cantor was wrong about cardinality --- (Correction) peteolcott <Here@Home> - 2019-09-17 14:09 -0500
Re: Cantor was wrong about cardinality --- (Correction) Fred <Fred@nowhere.invalid> - 2019-09-17 20:33 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-17 11:42 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 14:01 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 20:29 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 17:51 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-18 17:55 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-17 15:58 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 04:36 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:27 +0100
Re: Cantor was wrong about cardinality --- (Mike Terry Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:46 -0500
Re: Cantor was wrong about cardinality --- (Mike Terry Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:00 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:23 +0100
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:52 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:55 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:09 +0100
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:22 +0100
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Keith Thompson <kst-u@mib.org> - 2019-09-19 14:44 -0700
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] peteolcott <Here@Home> - 2019-09-19 17:31 -0500
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-20 14:11 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 19:47 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 18:16 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:02 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 18:08 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 01:49 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 20:01 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 03:25 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-16 22:39 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:26 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-17 11:55 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Python <python@invalid> - 2019-09-17 18:59 +0200
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 04:01 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-17 22:23 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 05:19 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Keith Thompson <kst-u@mib.org> - 2019-09-18 01:39 -0700
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 09:59 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-18 09:21 -0600
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 10:41 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Keith Thompson <kst-u@mib.org> - 2019-09-18 13:55 -0700
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-18 16:17 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 23:09 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 23:02 +0100
Re: Cantor was wrong about cardinality --- [ CONCURRENCE ] peteolcott <Here@Home> - 2019-09-18 11:10 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 18:39 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 12:15 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 10:37 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 16:56 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:27 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 16:43 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:51 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 18:12 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 09:05 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 10:49 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 10:02 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:18 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 23:24 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 10:01 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:13 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:56 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:40 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 11:03 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 12:48 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 12:25 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 22:35 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 16:42 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-14 22:54 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:28 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 11:34 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-14 18:05 +0100
Re: Cantor was wrong about cardinality --- COMPLETE (Andy Goofed) peteolcott <Here@Home> - 2019-09-14 18:00 -0500
Re: Cantor was wrong about cardinality --- COMPLETE (Andy Goofed) Fred <Fred@nowhere.invalid> - 2019-09-15 02:04 +0100
Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) peteolcott <Here@Home> - 2019-09-16 09:42 -0500
Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:13 -0600
Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) Fred <Fred@nowhere.invalid> - 2019-09-16 16:15 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 01:26 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 19:32 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 19:36 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 02:26 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:54 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 21:38 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:14 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 22:45 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 12:53 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-16 10:21 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-16 16:27 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 00:35 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 11:53 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 02:22 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 17:04 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:10 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 23:16 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 10:09 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:41 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:36 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 11:14 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 13:03 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 19:08 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 12:34 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 16:38 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-14 22:49 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:00 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 16:45 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 16:57 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 02:30 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 00:53 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-14 00:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-17 11:33 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 17:14 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) George Greene <greeneg@email.unc.edu> - 2019-09-14 18:24 -0700
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:25 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-15 11:50 +0100
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) George Greene <greeneg@email.unc.edu> - 2019-09-11 20:55 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 23:15 -0500
Page 12 of 17 — ← Prev page 1 … 10 11 [12] 13 14 … 17 Next page →
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-17 08:23 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <qlq1le$686$3@news.albasani.net> |
| In reply to | #210850 |
On 16/09/2019 23:46, Keith Thompson wrote: > André G. Isaak <agisaak@gm.invalid> writes: > [...] >> I already replied to this post, but wanted to provide an alternative >> response in case you don't follow my earlier one. >> >> [A, B] is defined as all real numbers x such that A <= x <= B >> >> (A, B] is defined as all real numbers x such that A < x <= B >> >> What's important to realize here is that you don't get (A,B] by starting >> with [A,B] and 'removing the first point'. These are simply two >> different intervals. There is no operation involved in which you get one >> from the other. > > I disagree with that last statement, and would be interested in a > demonstration that I'm wrong about that. > > [A,B] is a set of real numbers. (A,B] can be constructed by taking > [A,B] and removing a single element, namely A, and similarily vice > versa. All members of (A,B] are members of [A,B], and there is > exactly one real number that is a member of [A,B] and not of (A,B]. > > Of course this doesn't imply that there's a "first element" of (A,B]. > There clearly isn't. (Pete has correctly recognized a contradiction, What contradiction is that? > but has grabbed onto the wrong end of it.) >
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 11:52 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <CuSdnb9275HCLx7AnZ2dnUU7-U_NnZ2d@giganews.com> |
| In reply to | #210850 |
On 9/16/2019 5:46 PM, Keith Thompson wrote:
> André G. Isaak <agisaak@gm.invalid> writes:
> [...]
>> I already replied to this post, but wanted to provide an alternative
>> response in case you don't follow my earlier one.
>>
>> [A, B] is defined as all real numbers x such that A <= x <= B
>>
>> (A, B] is defined as all real numbers x such that A < x <= B
>>
>> What's important to realize here is that you don't get (A,B] by starting
>> with [A,B] and 'removing the first point'. These are simply two
>> different intervals. There is no operation involved in which you get one
>> from the other.
>
> I disagree with that last statement, and would be interested in a
> demonstration that I'm wrong about that.
>
> [A,B] is a set of real numbers. (A,B] can be constructed by taking
> [A,B] and removing a single element, namely A, and similarily vice
> versa. All members of (A,B] are members of [A,B], and there is
> exactly one real number that is a member of [A,B] and not of (A,B].
>
[0,1] - (0,1] = {0} a single point on the number line.
Thus proving a difference (in length) of one point between the first
interval and the second interval.
In all of the years where the width of a single point has been defined
to be 0 it was defined incorrectly, the actual width is Infinitesimal.
Infinitesimals sometimes act as if they had zero width and other times
act as if they minimum width. This is similar to the dichotomy of the
particle versus wave theories of light.
> Of course this doesn't imply that there's a "first element" of (A,B].
> There clearly isn't. (Pete has correctly recognized a contradiction,
> but has grabbed onto the wrong end of it.)
>
We removed the first point of the interval leaving all of the
remaining points of the interval: [0,1] - (0,1] = {0}
When we encode (0,1] as [0[1], 1] we can not remove the
next point from this interval: [0[1],1] - {0[1]} = (0[1], 1]
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 11:55 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <CuSdnb5275GVLh7AnZ2dnUU7-U-dnZ2d@giganews.com> |
| In reply to | #211084 |
On 9/19/2019 11:52 AM, peteolcott wrote:
> On 9/16/2019 5:46 PM, Keith Thompson wrote:
>> André G. Isaak <agisaak@gm.invalid> writes:
>> [...]
>>> I already replied to this post, but wanted to provide an alternative
>>> response in case you don't follow my earlier one.
>>>
>>> [A, B] is defined as all real numbers x such that A <= x <= B
>>>
>>> (A, B] is defined as all real numbers x such that A < x <= B
>>>
>>> What's important to realize here is that you don't get (A,B] by starting
>>> with [A,B] and 'removing the first point'. These are simply two
>>> different intervals. There is no operation involved in which you get one
>>> from the other.
>>
>> I disagree with that last statement, and would be interested in a
>> demonstration that I'm wrong about that.
>>
>> [A,B] is a set of real numbers. (A,B] can be constructed by taking
>> [A,B] and removing a single element, namely A, and similarily vice
>> versa. All members of (A,B] are members of [A,B], and there is
>> exactly one real number that is a member of [A,B] and not of (A,B].
>>
>
> [0,1] - (0,1] = {0} a single point on the number line.
> Thus proving a difference (in length) of one point between the first
> interval and the second interval.
>
> In all of the years where the width of a single point has been defined
> to be 0 it was defined incorrectly, the actual width is Infinitesimal.
>
> Infinitesimals sometimes act as if they had zero width and other times
> act as if they minimum width. This is similar to the dichotomy of the
> particle versus wave theories of light.
>
>> Of course this doesn't imply that there's a "first element" of (A,B].
>> There clearly isn't. (Pete has correctly recognized a contradiction,
>> but has grabbed onto the wrong end of it.)
>>
>
> We removed the first point of the interval leaving all of the
> remaining points of the interval: [0,1] - (0,1] = {0}
Correction:
> When we encode (0,1] as [0[1], 1] we can NOW remove the
> next point from this interval: [0[1],1] - {0[1]} = (0[1], 1]
>
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-19 18:09 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <qm0cno$r6o$1@news.albasani.net> |
| In reply to | #211084 |
On 19/09/2019 17:52, peteolcott wrote:
> [0,1] - (0,1] = {0} a single point on the number line.
Is 0 the point, or {0}?
> Thus proving a difference (in length) of one point between the first
> interval and the second interval.
>
> In all of the years where the width of a single point has been defined
What definition is that? Where is it stated?
> to be 0 it was defined incorrectly, the actual width is Infinitesimal.
You are conflating a point *at* 0 and a point *having a size of* 0.
> Infinitesimals sometimes act as if they had zero width and other times
> act as if they minimum width.
Infinitesimal don't have width at all. They are numbers. There is a
theory of infinitesimals where, if x is an infinitesimal, x may be not
equal to 0, but x^2 = 0. If I thought you had a reading age above eight
I'd direct you to smooth infinitesimal analysis.
> We removed the first point of the interval leaving all of the
We remove the first point of the interval: [0,1] - {0} = (0,1]. You
don't care, do you? You just type at random.
> remaining points of the interval: [0,1] - (0,1] = {0}
> When we encode (0,1] as [0[1], 1] we can not remove the
You are misusing notation: (0,1] is a half open interval,
[anything,anything] is a closed interval. Your "encoding" equates
things which can't be equal.
> next point from this interval: [0[1],1] - {0[1]} = (0[1], 1]
>
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-19 18:22 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <qm0dg5$q0d$1@news.albasani.net> |
| In reply to | #211088 |
On 19/09/2019 18:09, Fred wrote:
> On 19/09/2019 17:52, peteolcott wrote:
>
>
>> [0,1] - (0,1] = {0} a single point on the number line.
>
> Is 0 the point, or {0}?
>
>> Thus proving a difference (in length) of one point between the first
>> interval and the second interval.
>>
>> In all of the years where the width of a single point has been defined
>
> What definition is that? Where is it stated?
>
>> to be 0 it was defined incorrectly, the actual width is Infinitesimal.
>
> You are conflating a point *at* 0 and a point *having a size of* 0.
>
>> Infinitesimals sometimes act as if they had zero width and other times
>> act as if they minimum width.
>
> Infinitesimal don't have width at all. They are numbers. There is a
> theory of infinitesimals where, if x is an infinitesimal, x may be not
> equal to 0, but x^2 = 0. If I thought you had a reading age above eight
> I'd direct you to smooth infinitesimal analysis.
Someone mentioned dual numbers recently. It's all lost on you.
>> We removed the first point of the interval leaving all of the
>
> We remove the first point of the interval: [0,1] - {0} = (0,1]. You
> don't care, do you? You just type at random.
>
>> remaining points of the interval: [0,1] - (0,1] = {0}
>> When we encode (0,1] as [0[1], 1] we can not remove the
>
> You are misusing notation: (0,1] is a half open interval,
> [anything,anything] is a closed interval. Your "encoding" equates
> things which can't be equal.
>
>> next point from this interval: [0[1],1] - {0[1]} = (0[1], 1]
>>
>
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| From | Keith Thompson <kst-u@mib.org> |
|---|---|
| Date | 2019-09-19 14:44 -0700 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <ln5zlo6jwe.fsf@kst-u.example.com> |
| In reply to | #211084 |
peteolcott <Here@Home> writes:
[SNIP]
The phrase "Keith Thompson Concurrence" in the title of the parent
article is a lie.
--
Keith Thompson (The_Other_Keith) kst-u@mib.org <http://www.ghoti.net/~kst>
Will write code for food.
void Void(void) { Void(); } /* The recursive call of the void */
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 17:31 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <d6udncuuBIQwnBnAnZ2dnUU7-a3NnZ2d@giganews.com> |
| In reply to | #211098 |
On 9/19/2019 4:44 PM, Keith Thompson wrote: > peteolcott <Here@Home> writes: > [SNIP] > > The phrase "Keith Thompson Concurrence" in the title of the parent > article is a lie. > That claim is proven to be counter-factual by the provided context. That I said you concur with me does not indicate that you totally agreed with every subtle nuance. The aspect that you did agree to forms the whole basis of my position: (1) Points on a number line immediately adjacent to each other can be conceived and differ by an infinitesimal value. On 9/16/2019 11:38 PM, Keith Thompson wrote: > I can imagine that *this* set has a least element. For example > we can define "iota" as an infinitesimal, something that is not a > real number but that has a location on the number line, directly > adjacent to the real number 0. It is greater than 0 and less than > any positive real number. (2) The intervals [A, B] - (A, B] = point: A. On 9/16/2019 5:46 PM, Keith Thompson wrote: > [A,B] is a set of real numbers. (A,B] can be constructed by taking > [A,B] and removing a single element, namely A, and similarily vice > versa. All members of (A,B] are members of [A,B], and there is > exactly one real number that is a member of [A,B] and not of (A,B]. From (1) and (2) the whole Infinitesimal number system is derived. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-20 14:11 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <qm2j6f$ttc$1@news.albasani.net> |
| In reply to | #211100 |
On 19/09/2019 23:31, peteolcott wrote:
> On 9/19/2019 4:44 PM, Keith Thompson wrote:
>> peteolcott <Here@Home> writes:
>> [SNIP]
>>
>> The phrase "Keith Thompson Concurrence" in the title of the parent
>> article is a lie.
>>
>
> That claim is proven to be counter-factual by the provided context.
>
> That I said you concur with me does not indicate that you totally
> agreed with every subtle nuance. The aspect that you did agree to
> forms the whole basis of my position:
>
> (1) Points on a number line immediately adjacent to each other can be
> conceived
> and differ by an infinitesimal value.
>
> On 9/16/2019 11:38 PM, Keith Thompson wrote:
> > I can imagine that *this* set has a least element. For example
> > we can define "iota" as an infinitesimal, something that is not a
> > real number but that has a location on the number line, directly
> > adjacent to the real number 0. It is greater than 0 and less than
> > any positive real number.
>
> (2) The intervals [A, B] - (A, B] = point: A.
Wrong. A set minus a set is a set. [A, B] minus (A, B] is {A}, not A.
> On 9/16/2019 5:46 PM, Keith Thompson wrote:
> > [A,B] is a set of real numbers. (A,B] can be constructed by taking
> > [A,B] and removing a single element, namely A, and similarily vice
> > versa. All members of (A,B] are members of [A,B], and there is
> > exactly one real number that is a member of [A,B] and not of (A,B].
>
> From (1) and (2) the whole Infinitesimal number system is derived.
>
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 19:47 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <qlolci$l83$1@news.albasani.net> |
| In reply to | #210828 |
On 16/09/2019 19:27, peteolcott wrote:
> Hence the correspondence between real numbers and open intervals on
> the number line is inconsistent.
What does that mean? *Two * real numbers, say a and b with a < b,
correspond to the interval (a,b).
> An open interval specifies its first point as immediately after
> a specified point with no points in-between.
No, the *definition* is as follows: (a,b) =df {x:a<x<b}. There is
nothing in "{x:a<x<b}" that says "immediately after".
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 18:16 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <qlog1i$p9$1@news.albasani.net> |
| In reply to | #210813 |
On 16/09/2019 17:22, peteolcott wrote:
> Since [0, 100) clearly specifies every point on the number line between
> 0 and 100 except 100
but including 0. Your use of "between" is non-standard.
> it is specifying the point immediately before 100
> as the last point of this interval with no points in-between this point
> and 100. THAT IS WHAT IT SAYS.
WHAT IT SAYS (if IT is [0, 100)) is this set: {x:0<x<=100}. There is
nothing in the notation {x:0<x<=100} that says there is anything
immediately before 100.
>
> This contradicts the definition of real numbers that specifies there
> is always a real number between every pair of real numbers.
Suppose there is something immediately before 100, call it y. Then y <
50 + y/2 < 100, so why isn't 50 + y/2 this thing immediately before 100?
You don't seem to know elementary arithmetic.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 11:02 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <RI2dnZdu_JSPL-LAnZ2dnUU7-I2dnZ2d@giganews.com> |
| In reply to | #210802 |
On 9/16/2019 10:26 AM, André G. Isaak wrote:
> On 2019-09-16 9:17 a.m., peteolcott wrote:
>> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>
>>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>>
>>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>>
>>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>>>> But this is a side issue.
>>>>>>>>
>>>>>>>> That is defining X = X + 1.
>>>>>>>
>>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>>> Making an open interval closed does no change the length.
>>>>>>
>>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>>> The first one is 0% to 100%
>>>>>> The second one is 0% to 99%
>>>>>
>>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>>
>>>> There are too many ways to correctly say this.
>>>> (0, 100] integers is 0 to 100
>>>> (0, 100) integers is 0 to 99
>>>
>>> No. Sadly, almost everything you post introduces new errors. There are
>>> no open intervals in the integers so using the () notation is silly.
>>>
>>> You can, of course, give it a meaning (as you have tried to do here) but
>>> even then you get it wrong. If the "open" end means the bound is
>>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>>
>>> Why switch to integers which have totally different properties?
>>>
>>>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>>>> (0, 1] a length of exactly 1.0
>>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>>
>>>>> It's not magic. Length is defined that way for a reason. As I have
>>>>> said time and time again, just call your notion PO-length, define it
>>>>> properly, and we can decide if we care about it or not.
>>>>>
>>>>
>>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>>> 0.0 to 100.0 not including the 100 is 0 to
>>>> 99.999999999999999999999999999999999999999... on to infinity
>>>
>>> I propose Ben's law: Every sufficiently long mathematical crank thread
>>> ends up "debating" whether 0.999... = 1 or not.
>>>
>>> No. 99.999... = 100 and you stated that 100 is not included.
>>>
>>> There is no notation for the largest real in the open interval (0, 100),
>>> not because no one has come up with a notation for it (that's trivial,
>>> but the words will do) but because there is no such number.
>>>
>>
>> Do you realize that you just said that the number line is defined with gaps?
>> There is either a contiguous set of points between 0 and 100 or there are
>> gaps between 0 and 100, those are the only two choices.
>
>
> No. You are describing a number line with gaps. He is not. If there were indeed some largest real in the interval (0,100) (let's call it L), then what number lies between L and 100? According to you, none. But, it is axiomatic that for the real numbers,
> for every x and every y if z < y then there exists some z such that x < z < y. This proves (by reductio ad absurdum) that there is no such number L.
>
> André
>
>
Since it is clear that (0,100) specifies every geometric point on the number
line between 0 and 100 except for 0 and 100 then it does specify the geometric
point immediately after 0 and the geometric point immediately before 100 with
no geometric points in-between.
If these geometric points are defined to be real numbers and real numbers
are defined to always be divisible by 2, then something about the way that
these things are defined is inherently inconsistent.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 18:08 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <qlofii$2au$1@news.albasani.net> |
| In reply to | #210811 |
On 16/09/2019 17:02, peteolcott wrote: > If these geometric points are defined to be real numbers and real numbers > are defined to always be divisible by 2, then something about the way that > these things are defined is inherently inconsistent. Since the real numbers *aren't* defined to always be divisible by 2, it can't be that non definition that leads to inconsistency. Find the real (_a_ real would be better) definition of real numbers and (if you can) deduce an inconsistency from that. It may be that the real numbers *are* always divisible by 2, but if so it follows from the (or a) definition, not from what you imagine the definition to be. Keep in mind that you failed Calc II. I've no idea what calc II is, but failing it shows a poor understanding of mathematics.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-17 01:49 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <87k1a7bvbq.fsf@bsb.me.uk> |
| In reply to | #210799 |
peteolcott <Here@Home> writes:
> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
<cut>
>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>> 0.0 to 100.0 not including the 100 is 0 to
>>> 99.999999999999999999999999999999999999999... on to infinity
>>
>> I propose Ben's law: Every sufficiently long mathematical crank thread
>> ends up "debating" whether 0.999... = 1 or not.
>>
>> No. 99.999... = 100 and you stated that 100 is not included.
>>
>> There is no notation for the largest real in the open interval (0, 100),
>> not because no one has come up with a notation for it (that's trivial,
>> but the words will do) but because there is no such number.
>
> Do you realize that you just said that the number line is defined with
> gaps?
I realise I overestimated your reasoning powers and, frankly, I did
not think that possible given the low estimation I originally had.
> There is either a contiguous set of points between 0 and 100 or there are
> gaps between 0 and 100, those are the only two choices.
No, there are other options. The reals form a continuum, but contiguous
means touching or adjacent, and no two real are adjacent. Have you ever
considered getting an education?
>> This fact follows trivially from the definition of an open set in a
>> metric space, or from the axioms of the reals, or from the first baby
>> steps in topology... Repeatedly referring to a provably non-existent
>> object is just silly.
>
> https://www.encyclopediaofmath.org/index.php/Interval_and_segment
> An interval (open interval) is a set of points on a line lying between
> two fixed points A and B, where A and B themselves are considered not
> to belong to the interval.
>
> This means that there is a first point and there is a last point of every
> open interval.
No it does not. Nothing on that page lets you conclude that. If you
knew what an open set was... Oh, sorry, that's me suggesting education
again.
> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
Only if your points do not form a continuum. The real interval (0, 100)
does, and it has no first and no last number.
I see now why you abandoned that thread where you said you'd explain
your notation by answering questions about it.
> (0,3] specifies a length of that is exactly one geometric point less
> than this [0,3].
(0, 3] and [0, 3] have the same length. You don't get to say what the
length of an interval is. You get to make up the notion of PO-length
and then we get to ask what you mean, if we can summon up any reason to
care enough to ask.
> Interpreted as integers
> (0,3] specifies {1,2,3}
> [0,3] specifies {0,1,2,3} which is 1.0 longer
The integers do not form a continuum and are trivially countable. And I
strongly discourage using the same notation for contiguous integer
subsets. There's enough ambiguity in your own notation. Let's not have
two meanings for (0, 3].
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 20:01 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <DOedncdA-ZLFrR3AnZ2dnUU7-W_NnZ2d@giganews.com> |
| In reply to | #210861 |
On 9/16/2019 7:49 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/15/2019 6:33 AM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> 0.0 to 100.0 including the 100 is 0 to 100.0 >>>> 0.0 to 100.0 not including the 100 is 0 to >>>> 99.999999999999999999999999999999999999999... on to infinity >>> >>> I propose Ben's law: Every sufficiently long mathematical crank thread >>> ends up "debating" whether 0.999... = 1 or not. >>> >>> No. 99.999... = 100 and you stated that 100 is not included. >>> >>> There is no notation for the largest real in the open interval (0, 100), >>> not because no one has come up with a notation for it (that's trivial, >>> but the words will do) but because there is no such number. >> >> Do you realize that you just said that the number line is defined with >> gaps? > > I realise I overestimated your reasoning powers and, frankly, I did > not think that possible given the low estimation I originally had. > >> There is either a contiguous set of points between 0 and 100 or there are >> gaps between 0 and 100, those are the only two choices. > > No, there are other options. The reals form a continuum, but contiguous > means touching or adjacent, and no two real are adjacent. Have you ever > considered getting an education? > >>> This fact follows trivially from the definition of an open set in a >>> metric space, or from the axioms of the reals, or from the first baby >>> steps in topology... Repeatedly referring to a provably non-existent >>> object is just silly. >> >> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >> An interval (open interval) is a set of points on a line lying between >> two fixed points A and B, where A and B themselves are considered not >> to belong to the interval. >> >> This means that there is a first point and there is a last point of every >> open interval. > > No it does not. Nothing on that page lets you conclude that. If you > knew what an open set was... Oh, sorry, that's me suggesting education > again. > >> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1]. > > Only if your points do not form a continuum. The real interval (0, 100) > does, and it has no first and no last number. [0, 100] has a first and last point and a first and last real number (0, 100) has a first and last point yet no first and last real number. When-so-ever we remove any portion from the front of the interval: [0, 100] It always has a first point. [0.5, 100] [0.1, 100] [0.0001, 100] [0.0000000000000001, 100] [0.000000000000...1, 100] (0, 100] -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-17 03:25 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <87y2ynacbo.fsf@bsb.me.uk> |
| In reply to | #210862 |
peteolcott <Here@Home> writes:
> On 9/16/2019 7:49 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
<cut>
>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
>>
>> Only if your points do not form a continuum. The real interval (0, 100)
>> does, and it has no first and no last number.
>
> [0, 100] has a first and last point and a first and last real number
Yes.
> (0, 100) has a first and last point yet no first and last real number.
No. For any real x in (0, 100) we can find smaller elements. In fact,
infinitely many: xy for every y in (0, 1) is smaller than x.
> When-so-ever we remove any portion from the front of the interval: [0, 100]
> It always has a first point.
No. It depends on whether the portion you remove is closed or only
half-closed:
> [0.5, 100]
This results from removing [0, 0.5) and therefore does indeed have a
least element. If you remove [0, 0.5] you get (0.5, 100] and, as you
now know, that set does /not/ have a least element.
> [0.1, 100]
> [0.0001, 100]
> [0.0000000000000001, 100]
> [0.000000000000...1, 100]
These, too, result from removing some half-open set.
> (0, 100]
This results from removing a closed set ({0}) and therefore does not
have a least element.
Don't you think you should pick a book about the real numbers now?
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 22:39 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <l8ydnWn97MjFyB3AnZ2dnUU7-fHNnZ2d@giganews.com> |
| In reply to | #210869 |
On 9/16/2019 9:25 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
> <cut>
>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
>>>
>>> Only if your points do not form a continuum. The real interval (0, 100)
>>> does, and it has no first and no last number.
>>
>> [0, 100] has a first and last point and a first and last real number
>
> Yes.
>
>> (0, 100) has a first and last point yet no first and last real number.
>
> No. For any real x in (0, 100) we can find smaller elements. In fact,
> infinitely many: xy for every y in (0, 1) is smaller than x.
There is a first point that cannot be identified with a real number.
It can ONLY be identified with the infinitesimal number: 0.0[1].
It only seems like there is no first point when trying to identify
this point with a real number.
>
>> When-so-ever we remove any portion from the front of the interval: [0, 100]
>> It always has a first point.
>
> No. It depends on whether the portion you remove is closed or only
> half-closed:
>
>> [0.5, 100]
>
> This results from removing [0, 0.5) and therefore does indeed have a
> least element. If you remove [0, 0.5] you get (0.5, 100] and, as you
> now know, that set does /not/ have a least element.
>
>> [0.1, 100]
>> [0.0001, 100]
>> [0.0000000000000001, 100]
>> [0.000000000000...1, 100]
>
> These, too, result from removing some half-open set.
>
>> (0, 100]
>
> This results from removing a closed set ({0}) and therefore does not
> have a least element.
>
> Don't you think you should pick a book about the real numbers now?
>
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-17 14:26 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <877e679hpu.fsf@bsb.me.uk> |
| In reply to | #210872 |
peteolcott <Here@Home> writes: > On 9/16/2019 9:25 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >> <cut> >>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1]. >>>> >>>> Only if your points do not form a continuum. The real interval (0, 100) >>>> does, and it has no first and no last number. >>> >>> [0, 100] has a first and last point and a first and last real number >> >> Yes. >> >>> (0, 100) has a first and last point yet no first and last real number. >> >> No. For any real x in (0, 100) we can find smaller elements. In fact, >> infinitely many: xy for every y in (0, 1) is smaller than x. > > There is a first point that cannot be identified with a real number. > It can ONLY be identified with the infinitesimal number: 0.0[1]. A notation you refused to explain when you saw the half-baked answers you gave to my initial questions were taking you into dangerous waters. You agree, it seems, that for the intervals everyone else cares about which are subsets or R, (0, 100) has no least element. Please confirm this. It matters. If you confirm it I can more on to ignoring PO-points and PO-intervals because no one cares about them until you can define. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 11:55 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <mpudndy-lMSWjRzAnZ2dnUU7-eWdnZ2d@giganews.com> |
| In reply to | #210908 |
On 9/17/2019 8:26 AM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/16/2019 9:25 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1]. >>>>> >>>>> Only if your points do not form a continuum. The real interval (0, 100) >>>>> does, and it has no first and no last number. >>>> >>>> [0, 100] has a first and last point and a first and last real number >>> >>> Yes. >>> >>>> (0, 100) has a first and last point yet no first and last real number. >>> >>> No. For any real x in (0, 100) we can find smaller elements. In fact, >>> infinitely many: xy for every y in (0, 1) is smaller than x. >> >> There is a first point that cannot be identified with a real number. >> It can ONLY be identified with the infinitesimal number: 0.0[1]. > > A notation you refused to explain when you saw the half-baked answers > you gave to my initial questions were taking you into dangerous waters. > > You agree, it seems, that for the intervals everyone else cares about > which are subsets or R, (0, 100) has no least element. Please confirm > this. It matters. If you confirm it I can more on to ignoring > PO-points and PO-intervals because no one cares about them until you > can define. > I don't spend much time on answers to people that have proven to be persistently disingenuous. These answers can be found in my replies to others. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Python <python@invalid> |
|---|---|
| Date | 2019-09-17 18:59 +0200 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <5d8110de$0$3541$426a34cc@news.free.fr> |
| In reply to | #210925 |
Demented crank, peteolcott wrote: ... > I don't spend much time on answers to people that have proven to be > persistently > disingenuous. These answers can be found in my replies to others. You are an insufferable idiot Pete. Sooo sad you are the only really existing conscience in the whole Universe...
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-18 04:01 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <87k1a68g03.fsf@bsb.me.uk> |
| In reply to | #210925 |
peteolcott <Here@Home> writes: > On 9/17/2019 8:26 AM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/16/2019 9:25 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >>>> >>>>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote: >>>>>> peteolcott <Here@Home> writes: >>>> <cut> >>>>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1]. >>>>>> >>>>>> Only if your points do not form a continuum. The real interval (0, 100) >>>>>> does, and it has no first and no last number. >>>>> >>>>> [0, 100] has a first and last point and a first and last real number >>>> >>>> Yes. >>>> >>>>> (0, 100) has a first and last point yet no first and last real number. >>>> >>>> No. For any real x in (0, 100) we can find smaller elements. In fact, >>>> infinitely many: xy for every y in (0, 1) is smaller than x. >>> >>> There is a first point that cannot be identified with a real number. >>> It can ONLY be identified with the infinitesimal number: 0.0[1]. >> >> A notation you refused to explain when you saw the half-baked answers >> you gave to my initial questions were taking you into dangerous waters. >> >> You agree, it seems, that for the intervals everyone else cares about >> which are subsets or R, (0, 100) has no least element. Please confirm >> this. It matters. If you confirm it I can more on to ignoring >> PO-points and PO-intervals because no one cares about them until you >> can define. Are you really try to avoid confirming this, or have you just stopped reading what people write? > I don't spend much time on answers to people that have proven to be persistently > disingenuous. These answers can be found in my replies to others. Don't be silly. You stopped answering because you hit a dead end. You could not even say what numbers could go in front of the [] part. Vagueness is the soul of crankery. Sane people with a new idea want to explain it in as much detail as it asked for. Cranks fight hard to avoid explaining and details at all. -- Ben.
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