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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
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 10:35 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <ePidnXnjxsujPR7AnZ2dnUU7-anNnZ2d@giganews.com> |
| In reply to | #211062 |
On 9/19/2019 9:27 AM, Andy Walker wrote: > On 19/09/2019 03:38, André G. Isaak wrote: >> As I already noted, *every* point on the real number line represents >> a real number. There are no gaps. More importantly, there is no >> "process" being repeated. I think you are viewing this somewhat like >> the following: if we start with some real (say 1.0), we split the >> line in half at 0.5, leaving us with two gaps which need to be filled >> with 0.25 and 0.75 and so forth. > > I think you're right, and Pete misunderstands an important > difference between maths and computing. We see this in his version > of what infinity is [and which seems to him to be the only possible > way to explain/define infinity]. He sees maths as being a process, > in which you start from somewhere and take steps, like constructing > a proof, to get to some endpoint, or at least to get near to it [eg > in the sense of numerical analysis]. He doesn't understand that the > real numbers just "are", they don't have to be built one by one. > > OTOH the construction of the surreals does at least partly > meet Pete's needs. Starting from nothing, you can construct 0 [from > the empty set, containing no numbers (as you don't yet have any)], > and then 1 and -1 [from the empty set and 0], and then 2, 1/2, -1/2 > and -2 [from 1, 0 and -1] and so on. But you never reach all the > reals that way, let alone infinity and infinitesimals, just as > Achilles never catches the tortoise if you insist on him taking it > step by step; the "paradox" can be resolved in the same way. > >> But that is simply not the case. The real number line refers to an >> object which is already replete with points. While we can talk about >> constructing it by some process, that is entirely unnecessary. When >> we split 1.0 in half at 0.5, we now have a shorter segment which is >> *already* completely filled will points, which has no gaps, and was >> always that way. > > If you do try to construct the reals by a sequential process, > you run into the problem that any computable process creating points > produces a set of measure zero, whereas of course an interval of > reals of length L has measure L. It's Pete's process that is making > all those gaps! Uncountably many reals are sitting there, out of his > reach. > >> But, even if your argument were legitimate (it isn't), your >> 'infinitesimal' wouldn't solve it. If you claim that 0.0[1] is the >> least positive number, you are claiming that you have a point 0, >> followed by another point, 0.0[1] which are separated by a distance >> of 0.0[1]. What occupies that 0.0[1] length of line segment between >> zero and 0.0[1]? Is that not a 'gap'? > > What is a "gap"? But Pete's infinitesimals don't solve his > problems anyway. Whether the reals are countable or uncountable, > numbers of form x[i] where x is a real and i an integer have an > obvious bijection with the reals, and the process can't be used to > fill in the gaps. > [0.0[1], 1.0[0]] specifies all of the adjacent points in this interval: (0, 1]. THERE IS THE INCONSISTENCY. (1) There cannot be a real number associated with the point immediately adjacent to 0.0 because real numbers must be divisible by 2 and single points are indivisible. (2) If there is no real number immediately adjacent to 0.0 then there is always a measurable gap after 0.0. By dividing the size of the gap by 2 it gets smaller and smaller yet never closes, there are always points in the gap that are unaccounted for. [0.0[1], ∞] or (0, ∞] specifies all of the points > 0.0 on the number line. The first point of the open interval is immediately adjacent to 0.0 because every point from 0.0 to ∞ is included in that interval besides 0.0. -- 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 16:46 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qm07so$4rt$1@news.albasani.net> |
| In reply to | #211077 |
On 19/09/2019 16:35, peteolcott wrote: > THERE IS THE INCONSISTENCY. > (1) There cannot be a real number associated with the point > immediately adjacent to 0.0 because real numbers must be divisible > by 2 and single points are indivisible. Dividing a number and dividing a point are two different operations. Did you really not know that? > > (2) If there is no real number immediately adjacent to 0.0 then > there is always a measurable gap after 0.0. By dividing the > size of the gap by 2 it gets smaller and smaller yet never closes, > there are always points in the gap that are unaccounted for. > > [0.0[1], ∞] or (0, ∞] specifies all of the points > 0.0 on the number line. > > The first point of the open interval is immediately adjacent to 0.0 because > every point from 0.0 to ∞ is included in that interval besides 0.0. >
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 11:42 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <leGdnbr22-JCMh7AnZ2dnUU7-SPNnZ2d@giganews.com> |
| In reply to | #211062 |
On 9/19/2019 11:00 AM, Eram semper recta wrote:
> On Wednesday, 18 September 2019 22:38:22 UTC-4, André G. Isaak wrote:
>> On 2019-09-18 2:56 p.m., peteolcott wrote:
>>> On 9/18/2019 3:38 PM, André G. Isaak wrote:
>>>> On 2019-09-18 2:29 p.m., peteolcott wrote:
>>>>> On 9/18/2019 3:14 PM, André G. Isaak wrote:
>>>>>> On 2019-09-18 1:45 p.m., peteolcott wrote:
>>>>>>> On 9/18/2019 2:30 PM, André G. Isaak wrote:
>>>>>>>> On 2019-09-18 1:12 p.m., peteolcott wrote:
>>>>>>>>> On 9/18/2019 1:59 PM, André G. Isaak wrote:
>>>>>>>>>> On 2019-09-18 12:49 p.m., peteolcott wrote:
>>>>>>>>>>> On 9/18/2019 1:36 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2019-09-18 12:10 p.m., peteolcott wrote:
>>>>>>>>>>>>> On 9/18/2019 11:42 AM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2019-09-18 10:26 a.m., peteolcott wrote:
>>>>>>>>>>>>>>> On 9/18/2019 11:14 AM, André G. Isaak wrote:
>>>>>>>>>>>>>>>> On 2019-09-18 10:00 a.m., peteolcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> <snip>
>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Infinitesimals with an offset specify the gaps between
>>>>>>>>>>>>>>>>> the real numbers.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> And do you have any evidence to support the existence of
>>>>>>>>>>>>>>>> such gaps?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The point immediately adjacent to 0.0 cannot be expressed
>>>>>>>>>>>>>>> as a Real number,
>>>>>>>>>>>>>>> it can be expression as this Infinitesimal: 0.0[1].
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That's not evidence for a gap. That's simply you claiming
>>>>>>>>>>>>>> there is a gap and then giving a name to something that you
>>>>>>>>>>>>>> claim fills this alleged gap. But unless you can show the
>>>>>>>>>>>>>> gap exists, there's nothing to fill.
>>>>>>>>>>>>> When you try to use Real numbers to locate the point X that is
>>>>>>>>>>>>> immediately adjacent to 0.0 there is always a measurable
>>>>>>>>>>>>> distance
>>>>>>>>>>>>> between 0.0 and X. A measurable distance is ALWAYS a gap, hence
>>>>>>>>>>>>> Real numbers always have gaps. Infinitesimals fill in all
>>>>>>>>>>>>> these gaps
>>>>>>>>>>>>> thus forming a superset of Reals.
>>>>>>>>>>>>
>>>>>>>>>>>> That 'gap' is full of real numbers (2^ℵ₀ of them). Which means
>>>>>>>>>>>> that X isn't actually adjacent to zero.
>>>>>>>>>>>
>>>>>>>>>>> If there are no points adjacent to zero then there is a gap
>>>>>>>>>>> that can be
>>>>>>>>>>> filled in with Infinitesimals. If there is no gap then there is
>>>>>>>>>>> a point
>>>>>>>>>>> adjacent to zero.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I've restored the questions on arithmetic which you snipped. It
>>>>>>>>>> would be nice if you actually addressed them.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The above is prerequisite to anything else.
>>>>>>>>> I insist that we actually get to the point instead of perpetually
>>>>>>>>> talking in circles.
>>>>>>>>
>>>>>>>> I've already addressed the above several times. There is no number
>>>>>>>> adjacent to zero. Any 'gap' in the line is filled with other real
>>>>>>>> numbers.
>>>>>>>
>>>>>>> Each one having their own gap.
>>>>>>
>>>>>> Which, again, is filled with real numbers. That is what 'densely
>>>>>> ordered' means.
>>>>>
>>>>> >> Each one having their own gap.
>>>>
>>>> <snip pointless repetition>
>>>>
>>>> If I were as childish as you are, I would simply repeat 'each of which
>>>> is filled with real numbers' over and over again.
>>>
>>> NEVER FRIGGING FILLED BECAUSE EACH REAL BRINGS ITS OWN GAP
>>> UNTIL THIS PROCESS IS REPEATED AN INFINITE NUMBER OF TIMES
>>> THEN A POINT IMMEDIATELY ADJACENT TO 0.0 IS DERIVED THUS
>>> PROVING ME CORRECT.
>>
>> As I already noted, *every* point on the real number line represents a
>> real number.
>
> That is utter rubbish. There is no such thing as a "real number" line. Do you even know what it means to reify a point on a line?
>
>
> https://www.linkedin.com/pulse/real-number-line-john-gabriel
>
>
>> There are no gaps.
>
> You can't even begin to talk about "gaps" because a line DOES NOT consist of points. A line is the DISTANCE between two points. The points are like road signs indicating how far the current point/location is from some origin.
>
> A point has NO size, dimension or extent. This is very well defined. The Ancient Greeks did not make any mistake in its definition. Only the morons who came after did not understand.
>
I disagree: [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.
> To learn more, study my free eBook:
>
> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
>
>> More importantly, there is no "process"
>> being repeated. I think you are viewing this somewhat like the
>> following: if we start with some real (say 1.0), we split the line in
>> half at 0.5, leaving us with two gaps which need to be filled with 0.25
>> and 0.75 and so forth.
>>
>> But that is simply not the case. The real number line refers to an
>> object which is already replete with points. While we can talk about
>> constructing it by some process, that is entirely unnecessary. When we
>> split 1.0 in half at 0.5, we now have a shorter segment which is
>> *already* completely filled will points, which has no gaps, and was
>> always that way.
>>
>> But, even if your argument were legitimate (it isn't), your
>> 'infinitesimal' wouldn't solve it. If you claim that 0.0[1] is the least
>> positive number, you are claiming that you have a point 0, followed by
>> another point, 0.0[1] which are separated by a distance of 0.0[1]. What
>> occupies that 0.0[1] length of line segment between zero and 0.0[1]? Is
>> that not a 'gap'?
>>
>> André
>>
>> --
>> To email remove 'invalid' & replace 'gm' with well known Google mail
>> service.
>
--
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 17:58 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qm0c3n$s76$1@news.albasani.net> |
| In reply to | #211082 |
On 19/09/2019 17:42, peteolcott wrote:
> I disagree: [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
> 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.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 12:43 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <JLadnbYNEsCsIx7AnZ2dnUU7-THNnZ2d@giganews.com> |
| In reply to | #211082 |
On 9/19/2019 12:04 PM, Eram semper recta wrote:
> On Thursday, 19 September 2019 12:42:18 UTC-4, peteolcott wrote:
>> On 9/19/2019 11:00 AM, Eram semper recta wrote:
>>> On Wednesday, 18 September 2019 22:38:22 UTC-4, André G. Isaak wrote:
>>>> On 2019-09-18 2:56 p.m., peteolcott wrote:
>>>>> On 9/18/2019 3:38 PM, André G. Isaak wrote:
>>>>>> On 2019-09-18 2:29 p.m., peteolcott wrote:
>>>>>>> On 9/18/2019 3:14 PM, André G. Isaak wrote:
>>>>>>>> On 2019-09-18 1:45 p.m., peteolcott wrote:
>>>>>>>>> On 9/18/2019 2:30 PM, André G. Isaak wrote:
>>>>>>>>>> On 2019-09-18 1:12 p.m., peteolcott wrote:
>>>>>>>>>>> On 9/18/2019 1:59 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2019-09-18 12:49 p.m., peteolcott wrote:
>>>>>>>>>>>>> On 9/18/2019 1:36 PM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2019-09-18 12:10 p.m., peteolcott wrote:
>>>>>>>>>>>>>>> On 9/18/2019 11:42 AM, André G. Isaak wrote:
>>>>>>>>>>>>>>>> On 2019-09-18 10:26 a.m., peteolcott wrote:
>>>>>>>>>>>>>>>>> On 9/18/2019 11:14 AM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>>> On 2019-09-18 10:00 a.m., peteolcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> <snip>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Infinitesimals with an offset specify the gaps between
>>>>>>>>>>>>>>>>>>> the real numbers.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> And do you have any evidence to support the existence of
>>>>>>>>>>>>>>>>>> such gaps?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The point immediately adjacent to 0.0 cannot be expressed
>>>>>>>>>>>>>>>>> as a Real number,
>>>>>>>>>>>>>>>>> it can be expression as this Infinitesimal: 0.0[1].
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> That's not evidence for a gap. That's simply you claiming
>>>>>>>>>>>>>>>> there is a gap and then giving a name to something that you
>>>>>>>>>>>>>>>> claim fills this alleged gap. But unless you can show the
>>>>>>>>>>>>>>>> gap exists, there's nothing to fill.
>>>>>>>>>>>>>>> When you try to use Real numbers to locate the point X that is
>>>>>>>>>>>>>>> immediately adjacent to 0.0 there is always a measurable
>>>>>>>>>>>>>>> distance
>>>>>>>>>>>>>>> between 0.0 and X. A measurable distance is ALWAYS a gap, hence
>>>>>>>>>>>>>>> Real numbers always have gaps. Infinitesimals fill in all
>>>>>>>>>>>>>>> these gaps
>>>>>>>>>>>>>>> thus forming a superset of Reals.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That 'gap' is full of real numbers (2^ℵ₀ of them). Which means
>>>>>>>>>>>>>> that X isn't actually adjacent to zero.
>>>>>>>>>>>>>
>>>>>>>>>>>>> If there are no points adjacent to zero then there is a gap
>>>>>>>>>>>>> that can be
>>>>>>>>>>>>> filled in with Infinitesimals. If there is no gap then there is
>>>>>>>>>>>>> a point
>>>>>>>>>>>>> adjacent to zero.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I've restored the questions on arithmetic which you snipped. It
>>>>>>>>>>>> would be nice if you actually addressed them.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The above is prerequisite to anything else.
>>>>>>>>>>> I insist that we actually get to the point instead of perpetually
>>>>>>>>>>> talking in circles.
>>>>>>>>>>
>>>>>>>>>> I've already addressed the above several times. There is no number
>>>>>>>>>> adjacent to zero. Any 'gap' in the line is filled with other real
>>>>>>>>>> numbers.
>>>>>>>>>
>>>>>>>>> Each one having their own gap.
>>>>>>>>
>>>>>>>> Which, again, is filled with real numbers. That is what 'densely
>>>>>>>> ordered' means.
>>>>>>>
>>>>>>> >> Each one having their own gap.
>>>>>>
>>>>>> <snip pointless repetition>
>>>>>>
>>>>>> If I were as childish as you are, I would simply repeat 'each of which
>>>>>> is filled with real numbers' over and over again.
>>>>>
>>>>> NEVER FRIGGING FILLED BECAUSE EACH REAL BRINGS ITS OWN GAP
>>>>> UNTIL THIS PROCESS IS REPEATED AN INFINITE NUMBER OF TIMES
>>>>> THEN A POINT IMMEDIATELY ADJACENT TO 0.0 IS DERIVED THUS
>>>>> PROVING ME CORRECT.
>>>>
>>>> As I already noted, *every* point on the real number line represents a
>>>> real number.
>>>
>>> That is utter rubbish. There is no such thing as a "real number" line. Do you even know what it means to reify a point on a line?
>>>
>>>
>>> https://www.linkedin.com/pulse/real-number-line-john-gabriel
>>>
>>>
>>>> There are no gaps.
>>>
>>> You can't even begin to talk about "gaps" because a line DOES NOT consist of points. A line is the DISTANCE between two points. The points are like road signs indicating how far the current point/location is from some origin.
>>>
>>> A point has NO size, dimension or extent. This is very well defined. The Ancient Greeks did not make any mistake in its definition. Only the morons who came after did not understand.
>>>
>>
>> I disagree: [0,1] - (0,1] = {0} a single point on the number line.
>
> No. {0} is not a point. It is meaningless because it is not a length. When we calibrate the *rational* number line with measures, "0" is just an invisible marker denoting no distance. All other points must be of distance > 0 and one must be able to calibrate the line with a measure, viz. number.
>
> In fact, you can't realise "0" at all unless you place a marker between distances that are greater than 0, for example:
>
> __|__
>
> The horizontal bar is the marker. There is no actual space between the two lines __ and __. As one they appear to be ____
>
>
You are getting confused by the notation.
[1, 2] - (1, 2] = {1} the single beginning point of the first interval
is excluded from the second interval making the second interval have one
less element than the first interval.
If you have the infinite set of every car that can possibly exist
besides the exact form of the 1987 Chevy Camaro LS then this set is
infinitesimally smaller than the set also having 1987 Chevy Camaro LS
even though both sets are infinite, the first set is defined to have
one less element than the second set.
>
>> Thus proving a difference (in length) of one point between the first
>> interval and the second interval.
>
> The origin is not a *distance*. It is merely a reference location/point.
>
>>
>> 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.
>
> Nonsense. There is no such thing as "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.
>
> Mythology.
>
>>
>>> To learn more, study my free eBook:
>>>
>>> https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view
>>>
>>>> More importantly, there is no "process"
>>>> being repeated. I think you are viewing this somewhat like the
>>>> following: if we start with some real (say 1.0), we split the line in
>>>> half at 0.5, leaving us with two gaps which need to be filled with 0.25
>>>> and 0.75 and so forth.
>>>>
>>>> But that is simply not the case. The real number line refers to an
>>>> object which is already replete with points. While we can talk about
>>>> constructing it by some process, that is entirely unnecessary. When we
>>>> split 1.0 in half at 0.5, we now have a shorter segment which is
>>>> *already* completely filled will points, which has no gaps, and was
>>>> always that way.
>>>>
>>>> But, even if your argument were legitimate (it isn't), your
>>>> 'infinitesimal' wouldn't solve it. If you claim that 0.0[1] is the least
>>>> positive number, you are claiming that you have a point 0, followed by
>>>> another point, 0.0[1] which are separated by a distance of 0.0[1]. What
>>>> occupies that 0.0[1] length of line segment between zero and 0.0[1]? Is
>>>> that not a 'gap'?
>>>>
>>>> André
>>>>
>>>> --
>>>> To email remove 'invalid' & replace 'gm' with well known Google mail
>>>> service.
>>>
>>
>>
>> --
>> Copyright 2019 Pete Olcott All rights reserved
>>
>> "Great spirits have always encountered violent
>> opposition from mediocre minds." Albert Einstein
>
--
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 19:34 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qm0hn7$f90$1@news.albasani.net> |
| In reply to | #211090 |
On 19/09/2019 18:43, peteolcott wrote:
> You are getting confused by the notation.
> [1, 2] - (1, 2] = {1} the single beginning point of the first interval
Is 1 a point or is {1} a point? People who (unwisely in my opinion)
write of the number line intend that there be a correspondence between
points and numbers. 1 is a number, {1} is not.
> is excluded from the second interval making the second interval have one
> less element than the first interval.
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-18 19:42 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qlttqd$thg$1@news.albasani.net> |
| In reply to | #211032 |
On 18/09/2019 19:10, peteolcott wrote: > When you try to use Real numbers to locate the point X that is "Real" is a misspelling, "real" is correct. > immediately adjacent to 0.0 there is always a measurable distance > between 0.0 and X. A measurable distance is ALWAYS a gap, hence There is no such X. > Real numbers always have gaps. Infinitesimals fill in all these gaps > thus forming a superset of Reals. A superset of an uncountable set is uncountable. >
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-18 18:16 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qltoq9$818$1@news.albasani.net> |
| In reply to | #210993 |
On 18/09/2019 06:59, peteolcott wrote: > If it is impossible to name the point immediately adjacent to 0.0 It isn't impossible. I shall name it "Felicity". I also call my neighbour's pet unicorn "Felicity". Do you think I thereby magic in to existence a unicorn next door? > and there are no gaps in the number line then naming is insufficient.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-18 18:12 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qltohs$7ji$1@news.albasani.net> |
| In reply to | #210991 |
On 18/09/2019 06:27, peteolcott wrote: > The point immediately adjacent to 0.0 cannot be represented by Reals. Why "Reals" and not "reals"? You haven't demonstrated that there is a point immediately adjacent to 0. > Everyone always assumes that it does not exist yet they make this > assumption entirely on the basis that it cannot be expressed as a real. It is not an assumption, it is a simple matter of arithmetic: If 0 < x then there is a y such that 0 < y < x. (Proof: let y be x/2.) If x earns the title "point immediately adjacent to 0" why doesn't y earn the title "point even more immediately adjacent to 0"?
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 10:24 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <W6edneonwuwrAB7AnZ2dnUU7-aPNnZ2d@giganews.com> |
| In reply to | #210991 |
On 9/19/2019 12:16 AM, Zelos Malum wrote: >> The point immediately adjacent to 0.0 cannot be represented by Reals. > Everyone always assumes that it does not exist yet they make this > assumption entirely on the basis that it cannot be expressed as a real. > > It doesn't exist because whichever you claim it is, I can divide by 2 and voila! Even closer. > >> If there is no point immediately adjacent to 0.0 this entails that an > infinitesimal gap must exist. If an infinitesimal gap does not exist > then there must be a point immediately adjacent to 0.0. > > Non-sequitor statements. > THERE IS THE INCONSISTENCY. (1) There cannot be a real number associated with the point immediately adjacent to 0.0 because real numbers must be divisible by 2 and single points are indivisible. (2) If there is no real number immediately adjacent to 0.0 then there is always a measurable gap after 0.0. By dividing the size of the gap by 2 it gets smaller and smaller yet never closes, there are always points in the gap that are unaccounted for. If no Real number is immediately adjacent to 0.0 then some other type of number would fill the gap because it is clear that Real numbers do not correspond to all of the points on the number line because they always leave gaps. -- 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 16:39 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (NO GAPS) |
| Message-ID | <qm07fe$6kl$1@news.albasani.net> |
| In reply to | #211076 |
On 19/09/2019 16:24, peteolcott wrote: > THERE IS THE INCONSISTENCY. > (1) There cannot be a real number associated with the point > immediately adjacent to 0.0 because real numbers must be divisible > by 2 and single points are indivisible. You are muddling numbers which can always be divided by 0, and points which are indivisible. That two different notions of division applied to two different things. If you ever want to learn some mathematics, I recommend Courant and Robbin's /What is mathematics/.
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-18 18:05 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qlto48$96p$1@news.albasani.net> |
| In reply to | #210975 |
On 18/09/2019 04:31, peteolcott wrote: > Infinity is a process rather than a value, thus there is no greatest > integer and all infinite sets are likewise this exact same limitlessness. > > Integer N = 0; > HERE: > N = N + 1; > goto HERE; That has nothing to do with infinity as discussed in this thread. In fact, the above code has nothing to do with any infinity, has it?
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| From | Exfalso Quodlibet <exflaso.quodlibet@gmail.com> |
|---|---|
| Date | 2019-09-17 20:41 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <270100f8-7056-462f-8ee9-1690a412c1b8@googlegroups.com> |
| In reply to | #210972 |
On Tuesday, September 17, 2019 at 11:19:58 PM UTC-4, peteolcott wrote: > 0.0[0] = 0.0 > 0.0[1] = the next point after 0.0 > 0.0[2] = 2 points after 0.0 > 0.0[3] = 3 points after 0.0 So, solve for k: 0.0[k] = 1.0 You claim that all the reals are countable, by using your infinitesimals, but all I can see so far is that you are "counting" a bunch of points arbitrarily close to 0.0, and never reaching any other real numbers. How can you count all the reals if your counting method never gets you far enough away from 0.0 to even reach 1.0 (let alone 10.0, 100.0, etc.)? By the way, Peter Olcott is still a pedophile: https://www.wowt.com/home/headlines/Papillion-Man-Faces-71-Counts-of-Child-Pornography-Possession-297743591.html EFQ
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-18 05:15 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <875zlq8cl4.fsf@bsb.me.uk> |
| In reply to | #210972 |
peteolcott <Here@Home> writes:
> On 9/17/2019 9:55 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
<cut>
>>> Keith Thompson understands that they could refute differing sized
>>> cardinality of infinite sets.
>>
>> No he doesn't. The trouble is, you don't understand what he's saying.
>> In fact he agrees with me though he puts it more cautiously. I'll leave
>> it here for those that /can/ follow:
>
> I SUMMED IT UP MORE CONCISELY HERE:
>
> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
Not on "the" number line (that's just the reals ordered by magnitude)
but on the PO-number line (as yet not well specified). Of course you
can define a set with such a point but that does not refute Cantor.
> On 9/16/2019 11:38 PM, Keith Thompson wrote:
>> 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.
>
> WE CAN SUBTRACT A SINGLE POINT FROM AN INTERVAL DERIVING ANOTHER
> INTERVAL THAT DOES NOT HAVE THIS POINT
That's trivially obvious (if you have the axiom of choice) and does not
refute Cantor either. The question you can't address is how, or even
whether, the countable set of points so removed, one by one, is equal to
the whole set. This picking off of points does not refute Cantor unless
every real occurs at some stage in the step by step removing of points.
You can't prove that they do, and we can prove they don't.
I know this point will baffle you. I apologise in advance. I also note
for others that you did not specify the ordering being used and I don't
really care because all orderings of points (in the usual sense) fail in
the same way.
> Mike Terry agreed with this verbatim: [A, B] - {A} = (A, B]
Ha! Of course he did. You did not see when I stated it as well, did
you? Maybe you did not recognise the notation I used.
> Infinitesimal Numbers would encode (A, B] as [A[1], B]
>
> We merely extrapolate the very next elaboration
> [A[1], B] - {A[1]} = (A[1], B] encoded as [A[2], B]
>
> This shows how Infinitesimal Numbers directly reference immediately
> adjacent points on a number line.
>
> 0.0[0] = 0.0
> 0.0[1] = the next point after 0.0
> 0.0[2] = 2 points after 0.0
> 0.0[3] = 3 points after 0.0
Yes, everyone gets that this is your plan. The trouble is you won't
answer the questions that would enable you to learn why you are wrong.
I offered, and you appeared to want to answer them, but that lasted
exactly one post! You clammed up on all of my follow ups, so I must
assume you don't want to know why your PO-points say nothing about
Cantor.
In short, you are wrong either because your PO-points don't include the
reals (or something just like them), so the fact that they are countable
has no impact on Cantor's result, or you are wrong because your
PO-points /do/ include the reals (or something just like them) and they
can't be enumerated like you say.
Of course to you it is simple obvious that every set can be enumerated
by picking the elements, one by one, in some order or other. This will
be a major sticking point.
A feature that makes discussing things with you very tedious is that you
assume everyone else is as slow as you are, but this idea of picking off
the numbers one by one was clear from your very first post. You simply
did not address any of the obvious problems with it.
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 23:32 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <xLOdnXgeYsLQLhzAnZ2dnUU7-eHNnZ2d@giganews.com> |
| In reply to | #210980 |
On 9/17/2019 11:15 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/17/2019 9:55 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> Keith Thompson understands that they could refute differing sized >>>> cardinality of infinite sets. >>> >>> No he doesn't. The trouble is, you don't understand what he's saying. >>> In fact he agrees with me though he puts it more cautiously. I'll leave >>> it here for those that /can/ follow: >> >> I SUMMED IT UP MORE CONCISELY HERE: >> >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > > Not on "the" number line (that's just the reals ordered by magnitude) > but on the PO-number line (as yet not well specified). Of course you > can define a set with such a point but that does not refute Cantor. > Sure it does because other number systems cannot account for ALL of the points on the number line. Since the ONLY number system that can account for ALL the points on the number line forms a bijection to ALL these points indexed by integers, there is a bijection between integers and ALL these points. Because infinity is a process rather than any value: Integer N = 0; HERE: N = N + 1; goto HERE; It is pretty silly to envision any infinite set that is "larger" than any other infinite set. >> On 9/16/2019 11:38 PM, Keith Thompson wrote: >>> 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. >> -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-17 23:21 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qlsesd$saj$1@dont-email.me> |
| In reply to | #210985 |
On 2019-09-17 10:32 p.m., peteolcott wrote: > On 9/17/2019 11:15 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/17/2019 9:55 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >> <cut> >>>>> Keith Thompson understands that they could refute differing sized >>>>> cardinality of infinite sets. >>>> >>>> No he doesn't. The trouble is, you don't understand what he's saying. >>>> In fact he agrees with me though he puts it more cautiously. I'll >>>> leave >>>> it here for those that /can/ follow: >>> >>> I SUMMED IT UP MORE CONCISELY HERE: >>> >>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> >> Not on "the" number line (that's just the reals ordered by magnitude) >> but on the PO-number line (as yet not well specified). Of course you >> can define a set with such a point but that does not refute Cantor. >> > > Sure it does because other number systems cannot account for ALL > of the points on the number line. > > Since the ONLY number system that can account for ALL the points > on the number line forms a bijection to ALL these points indexed > by integers, there is a bijection between integers and ALL these points. How does this indexing work? If there is a bijection, what is that bijection? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-18 18:42 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87h8597b7v.fsf@bsb.me.uk> |
| In reply to | #210985 |
peteolcott <Here@Home> writes: > On 9/17/2019 11:15 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/17/2019 9:55 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >> <cut> >>>>> Keith Thompson understands that they could refute differing sized >>>>> cardinality of infinite sets. >>>> >>>> No he doesn't. The trouble is, you don't understand what he's saying. >>>> In fact he agrees with me though he puts it more cautiously. I'll leave >>>> it here for those that /can/ follow: >>> >>> I SUMMED IT UP MORE CONCISELY HERE: >>> >>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> >> Not on "the" number line (that's just the reals ordered by magnitude) >> but on the PO-number line (as yet not well specified). Of course you >> can define a set with such a point but that does not refute Cantor. > > Sure it does because other number systems cannot account for ALL > of the points on the number line. Cantor proved the real are uncountable. The theorem stands even if they don't "account for ALL of the points on the number line". The theorem is about the reals. > Since the ONLY number system that can account for ALL the points > on the number line forms a bijection to ALL these points indexed > by integers, there is a bijection between integers and ALL these > points. The reals remain uncountable no matter how much you show your ignorance of what might or might not constitute "points on the number line". To refute Cantor you need to show a bijection between N (or Z) and R. > Because infinity is a process rather than any value: > > Integer N = 0; > HERE: > N = N + 1; > goto HERE; > > It is pretty silly to envision any infinite set that is "larger" > than any other infinite set. Ah, the argument from what someone with mental health issues considers silly. That carries no weight with mathematicians. There is no surjective function from N onto R. This is a proved fact. Stop pretending you have the knowledge to even know what this means, let alone refute it. I repeat my offer to show you why you are wrong, but you would have to be prepared to both explain and learn. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 12:58 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <lf2dnS1XPbvb7R_AnZ2dnUU7-V_NnZ2d@giganews.com> |
| In reply to | #211026 |
On 9/18/2019 12:42 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/17/2019 11:15 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/17/2019 9:55 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> Keith Thompson understands that they could refute differing sized >>>>>> cardinality of infinite sets. >>>>> >>>>> No he doesn't. The trouble is, you don't understand what he's saying. >>>>> In fact he agrees with me though he puts it more cautiously. I'll leave >>>>> it here for those that /can/ follow: >>>> >>>> I SUMMED IT UP MORE CONCISELY HERE: >>>> >>>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >>> >>> Not on "the" number line (that's just the reals ordered by magnitude) >>> but on the PO-number line (as yet not well specified). Of course you >>> can define a set with such a point but that does not refute Cantor. >> >> Sure it does because other number systems cannot account for ALL >> of the points on the number line. > > Cantor proved the real are uncountable. The theorem stands even if they > don't "account for ALL of the points on the number line". The theorem > is about the reals. > If Infinitesimals indexed by integers can count ALL of the numbers on the number line including the subset of numbers that are Reals then Cantor is refuted. That Integers cannot count the Real directly yet can count them indirectly does not actually indicate a difference in the "size" of the sets, it merely indicates an incompatibility between Reals and Integers. >> Since the ONLY number system that can account for ALL the points >> on the number line forms a bijection to ALL these points indexed >> by integers, there is a bijection between integers and ALL these >> points. > > The reals remain uncountable no matter how much you show your ignorance > of what might or might not constitute "points on the number line". To > refute Cantor you need to show a bijection between N (or Z) and R. > >> Because infinity is a process rather than any value: >> >> Integer N = 0; >> HERE: >> N = N + 1; >> goto HERE; >> >> It is pretty silly to envision any infinite set that is "larger" >> than any other infinite set. > > Ah, the argument from what someone with mental health issues considers > silly. That carries no weight with mathematicians. There is no > surjective function from N onto R. This is a proved fact. Stop > pretending you have the knowledge to even know what this means, let > alone refute it. > > I repeat my offer to show you why you are wrong, but you would have to > be prepared to both explain and learn. > You can't show me where I am wrong you can ONLY show that a different set of assumptions leads to a different conclusion. -- 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 | 2019-09-18 19:05 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qltrkg$14u$1@news.albasani.net> |
| In reply to | #211030 |
On 18/09/2019 18:58, peteolcott wrote: > If Infinitesimals indexed by integers can count ALL of the numbers > on the number line including the subset of numbers that are Reals > then Cantor is refuted. > > That Integers cannot count the Real directly yet can count them > indirectly does not actually indicate a difference in the "size" > of the sets, it merely indicates an incompatibility between Reals > and Integers. If a set is uncountable then every superset of it is uncountable.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-19 01:42 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87v9tp5d7c.fsf@bsb.me.uk> |
| In reply to | #211030 |
peteolcott <Here@Home> writes: > On 9/18/2019 12:42 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: <cut> >>> Sure it does because other number systems cannot account for ALL >>> of the points on the number line. >> >> Cantor proved the real are uncountable. The theorem stands even if they >> don't "account for ALL of the points on the number line". The theorem >> is about the reals. > > If Infinitesimals indexed by integers can count ALL of the numbers > on the number line including the subset of numbers that are Reals > then Cantor is refuted. Of course. In fact if you can do that you can simplify matters by counting ONLY those that are reals. That's the daft thing: most of your infinitesimals are just a side show. Throw away all of your infinitesimals that are not reals and count the result (you can't). > That Integers cannot count the Real directly yet can count them > indirectly does not actually indicate a difference in the "size" of > the sets, it merely indicates an incompatibility between Reals and > Integers. Well if this waffle means you can can't count the reals, you have not refuted anything. By all means show a surjective function from Z to some set that includes the reals as special cases and I'll publish a better paper with a direct surjection from N to R. (Neither is possible, by the way.) The astute reader will note that we are still missing the bijection you claim. Mind you, we are still missing the impossible Turing machine you claimed to have in December last year, so I'm not holding my breath for any of this. You never show any of the magic rainbow sparkle ponies you claim to have. <cut> >>> It is pretty silly to envision any infinite set that is "larger" >>> than any other infinite set. >> >> Ah, the argument from what someone with mental health issues considers >> silly. That carries no weight with mathematicians. There is no >> surjective function from N onto R. This is a proved fact. Stop >> pretending you have the knowledge to even know what this means, let >> alone refute it. >> >> I repeat my offer to show you why you are wrong, but you would have to >> be prepared to both explain and learn. > > You can't show me where I am wrong I can show any intelligent person that you are wrong about Cantor's theorem simply by showing them the proof of Cantor's theorem. And if you ever publish a claimed surjective function from Z (or any countable set) to any set the includes the reals, I will show that intelligent person where you went wrong. And I'll also show them what you've got wrong about Turning machines it you ever post that impossible TM you've boasted about having for months and months. But you are not prepared to explain yourself and not open to asking question when you don't understand an explanation. You can't learning anything problematic that way so I think you are right about my not being able to to show /you/ where you are wrong. For example, I've explained that your picking off points, one by one, in any order at all from any set that includes the reals can't ever count that set, but you never even commented on that much less asked any intelligent questions to find out more. You just don't want to know why you are wrong. You just want to keep boasting. > you can ONLY show that > a different set of assumptions leads to a different conclusion. That's what you've spent most of the last two decades doing: talking about things using the usual terms (to hook people in) and then, when pressed, you pretend that you always meant things to be defined how you'd like them to be. Define PO-truth as just entailment and, poof!, you get what you want. The PO-numbers can be "based on zero" and written as 0[k] with k in Z and, poof!, the "numbers" are countable. It's so incredible shallow, but then being right is not your objective here, is it? -- Ben.
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