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Groups > comp.ai.philosophy > #18797 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-08-08 12:15 -0500 |
| Last post | 2019-09-11 17:31 -0700 |
| Articles | 20 on this page of 244 — 17 participants |
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Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-08-08 12:15 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-08-08 21:28 +0100
Re: Provably unprovable eliminates incompleteness Dhu on Gate <campbell@neotext.ca> - 2019-09-08 06:06 +0000
Re: Provably unprovable eliminates incompleteness Stuart Redmann <DerTopper@web.de> - 2019-09-09 11:30 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 10:01 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-09 21:38 +0100
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 18:05 -0500
Re: Provably unprovable eliminates incompleteness David Brown <david.brown@hesbynett.no> - 2019-09-10 09:01 +0200
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-10 10:38 -0500
Re: Provably unprovable eliminates incompleteness David Brown <david.brown@hesbynett.no> - 2019-09-10 22:01 +0200
Re: Provably unprovable eliminates incompleteness [ Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-10 20:12 -0500
Re: Provably unprovable eliminates incompleteness Reinhardt Behm <rbehm@hushmail.com> - 2019-09-11 15:31 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:04 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Reinhardt Behm <rbehm@hushmail.com> - 2019-09-12 10:20 +0800
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 23:51 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Keith Thompson <kst-u@mib.org> - 2019-09-12 01:22 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:05 -0500
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) peteolcott <Here@Home> - 2019-09-11 20:03 -0500
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) peteolcott <Here@Home> - 2019-09-11 22:16 -0500
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) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-12 21:00 -0500
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 peteolcott <Here@Home> - 2019-09-13 11:48 -0500
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 13:09 -0500
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 19:24 -0500
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? 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 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 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 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 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 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). 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 (Concurrence) peteolcott <Here@Home> - 2019-09-17 11:20 -0500
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 --- 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 peteolcott <Here@Home> - 2019-09-17 17:51 -0500
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 --- (Mike Terry Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:46 -0500
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 ] 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 --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 11:02 -0500
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? peteolcott <Here@Home> - 2019-09-16 22:39 -0500
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? 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 --- [ CONCURRENCE ] peteolcott <Here@Home> - 2019-09-18 11:10 -0500
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) 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 (Andy Goofed) peteolcott <Here@Home> - 2019-09-14 18:00 -0500
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 peteolcott <Here@Home> - 2019-09-14 19:36 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 21:38 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-16 10:21 -0500
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 LIED !!! peteolcott <Here@Home> - 2019-09-14 00:55 -0500
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) peteolcott <Here@Home> - 2019-09-16 18:24 -0500
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) 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) peteolcott <Here@Home> - 2019-09-19 10:35 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 11:42 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 12:43 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:24 -0500
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) peteolcott <Here@Home> - 2019-09-19 17:13 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 19:49 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 09:45 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Don Stockbauer <donstockbauer@hotmail.com> - 2019-09-27 07:24 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-12 22:07 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-12 18:53 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-12 17:47 -0700
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-13 08:14 +0000
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-13 09:35 -0500
Re: Provably unprovable eliminates incompleteness Mr Flibble <flibble@i42.removethisbit.co.uk> - 2019-09-13 15:55 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 13:35 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 22:52 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:18 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-14 23:30 +0100
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] peteolcott <Here@Home> - 2019-09-14 17:42 -0500
Re: Provably unprovable eliminates incompleteness--- [ Cantor was wrong about cardinality ] Jeff Barnett <jbb@notatt.com> - 2019-09-14 18:12 -0600
Re: Provably unprovable eliminates incompleteness Juha Nieminen <nospam@thanks.invalid> - 2019-09-15 08:09 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:50 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:13 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 11:24 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 17:30 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 12:08 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 18:15 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 13:35 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 20:02 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 14:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-16 22:26 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:11 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 18:12 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:11 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-17 21:10 +0200
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 14:30 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 14:33 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] Keith Thompson <kst-u@mib.org> - 2019-09-17 13:28 -0700
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 15:31 -0500
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 22:16 +0100
Re: Provably unprovable eliminates incompleteness [ Keith and Mike basis for Infinitesimal numbers ] peteolcott <Here@Home> - 2019-09-17 16:42 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-17 08:05 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 11:45 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 18:14 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 12:36 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 19:45 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-17 20:09 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 14:14 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 18:59 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 11:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-17 13:48 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Keith Thompson <kst-u@mib.org> - 2019-09-17 12:01 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 07:35 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 10:02 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:25 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:41 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-18 22:56 +0100
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-18 21:34 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-18 16:42 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-19 17:54 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 13:26 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:06 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:37 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:07 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:04 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 17:32 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:10 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:33 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 16:05 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:48 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-19 18:00 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 08:52 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-20 00:10 -0700
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] David Brown <david.brown@hesbynett.no> - 2019-09-20 10:11 +0200
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] Juha Nieminen <nospam@thanks.invalid> - 2019-09-20 08:25 +0000
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] peteolcott <Here@Home> - 2019-09-16 09:54 -0500
Re: Provably unprovable eliminates incompleteness [ All infinite sets have the same cardinality ] André G. Isaak <agisaak@gm.invalid> - 2019-09-16 09:15 -0600
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 13:13 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:54 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:09 -0500
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:45 -0700
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:34 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 14:58 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 15:57 -0700
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] peteolcott <Here@Home> - 2019-09-19 18:10 -0500
Re: Provably unprovable eliminates incompleteness [ COMPLETE-2 ] Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> - 2019-09-20 13:18 +0100
Re: Provably unprovable eliminates incompleteness Louis Valence <lvalence@example.com> - 2019-09-09 17:43 -0300
Re: Provably unprovable eliminates incompleteness Siri Cruise <chine.bleu@yahoo.com> - 2019-09-19 12:28 -0700
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-19 15:04 -0500
Re: Provably unprovable eliminates incompleteness peteolcott <Here@Home> - 2019-09-09 09:57 -0500
Re: Provably unprovable eliminates incompleteness Keith Thompson <kst-u@mib.org> - 2019-09-09 13:30 -0700
Re: Provably unprovable eliminates incompleteness temakoutera62@gmail.com - 2019-09-11 17:31 -0700
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-08-08 12:15 -0500 |
| Subject | Provably unprovable eliminates incompleteness |
| Message-ID | <YdmdnSGX1cpdxdHAnZ2dnUU7-WXNnZ2d@giganews.com> |
"This sentence is unprovable" can be proven to be unprovable on the basis that its satisfaction derives a contradiction. Proof that Wittgenstein is correct about Gödel https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mr Flibble <flibbleREMOVETHISBIT@i42.co.uk> |
|---|---|
| Date | 2019-08-08 21:28 +0100 |
| Message-ID | <3C%2F.5$3s7.3@fx01.fr7> |
| In reply to | #18797 |
On 08/08/2019 18:15, peteolcott wrote: > "This sentence is unprovable" can be proven to be unprovable > on the basis that its satisfaction derives a contradiction. > > Proof that Wittgenstein is correct about Gödel > https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel Modulo the Sausage Conjecture of course. /Flibble -- "Snakes didn't evolve, instead talking snakes with legs changed into snakes." - Rick C. Hodgin “You won’t burn in hell. But be nice anyway.” – Ricky Gervais “I see Atheists are fighting and killing each other again, over who doesn’t believe in any God the most. Oh, no..wait.. that never happens.” – Ricky Gervais "Suppose it's all true, and you walk up to the pearly gates, and are confronted by God," Bryne asked on his show The Meaning of Life. "What will Stephen Fry say to him, her, or it?" "I'd say, bone cancer in children? What's that about?" Fry replied. "How dare you? How dare you create a world to which there is such misery that is not our fault. It's not right, it's utterly, utterly evil." "Why should I respect a capricious, mean-minded, stupid God who creates a world that is so full of injustice and pain. That's what I would say."
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| From | Dhu on Gate <campbell@neotext.ca> |
|---|---|
| Date | 2019-09-08 06:06 +0000 |
| Message-ID | <ql25og$fnm$1@news.albasani.net> |
| In reply to | #18797 |
On Thu, 08 Aug 2019 12:15:48 -0500, peteolcott wrote: > "This sentence is unprovable" can be proven to be unprovable > on the basis that its satisfaction derives a contradiction. > > Proof that Wittgenstein is correct about Gödel > https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel Since this is unreadable by peons, I can only speculate, but provably unprovable sounds like a useless tautology. Dhu -- Je suis Canadien. Ce n'est pas Francais ou Anglaise. C'est une esp`ece de sauvage: ne obliviscaris, vix ea nostra voco;-) http://babayaga.neotext.ca/PublicKeys/Duncan_Patton_a_Campbell_pubkey.txt
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| From | Stuart Redmann <DerTopper@web.de> |
|---|---|
| Date | 2019-09-09 11:30 +0200 |
| Message-ID | <581781046.589713241.741596.DerTopper-web.de@news.eternal-september.org> |
| In reply to | #19086 |
Dhu on Gate <campbell@neotext.ca> wrote: > On Thu, 08 Aug 2019 12:15:48 -0500, peteolcott wrote: > >> "This sentence is unprovable" can be proven to be unprovable >> on the basis that its satisfaction derives a contradiction. >> >> Proof that Wittgenstein is correct about Gödel >> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel > > > Since this is unreadable by peons, I can only speculate, > but provably unprovable sounds like a useless tautology. > > Dhu > It isn't. It rather shows that - like the speed of light in physics - there are some rather unexpected limitations to what is possible in mathematics. For many years mathematicians believed that, given a set of axioms, every possible theorem in the given field can be proven to be either true or false based on logical deduction from these axioms. Goedel showed that this is not always the case (see the continuum hypothesis). This implies that there are things in mathematics that cannot be proven. This culminated in Goedels incompleteness theorem, which is considered by many mathematicians as a severe throwback in maths. Regards, Stuart
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-09 10:01 -0500 |
| Message-ID | <T9mdnX__WZbR9OvAnZ2dnUU7-R_NnZ2d@giganews.com> |
| In reply to | #19087 |
On 9/9/2019 4:30 AM, Stuart Redmann wrote: > Dhu on Gate <campbell@neotext.ca> wrote: >> On Thu, 08 Aug 2019 12:15:48 -0500, peteolcott wrote: >> >>> "This sentence is unprovable" can be proven to be unprovable >>> on the basis that its satisfaction derives a contradiction. >>> >>> Proof that Wittgenstein is correct about Gödel >>> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel >> >> >> Since this is unreadable by peons, I can only speculate, >> but provably unprovable sounds like a useless tautology. >> >> Dhu >> > > It isn't. It rather shows that - like the speed of light in physics - there > are some rather unexpected limitations to what is possible in mathematics. > For many years mathematicians believed that, given a set of axioms, every > possible theorem in the given field can be proven to be either true or > false based on logical deduction from these axioms. > > Goedel showed that this is not always the case (see the continuum > hypothesis). This implies that there are things in mathematics that cannot > be proven. This culminated in Goedels incompleteness theorem, which is > considered by many mathematicians as a severe throwback in maths. > > Regards, > Stuart > https://en.wikipedia.org/wiki/Continuum_hypothesis It turns out that the basis concept of cardinality is ill-formed. All infinities are the same size. The number of real numbers is the number of adjacent geometric points on a number line, countable using integers. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Mr Flibble <flibble@i42.removethisbit.co.uk> |
|---|---|
| Date | 2019-09-09 21:38 +0100 |
| Message-ID | <dLydF.116034$Gz5.16238@fx08.fr7> |
| In reply to | #19089 |
On 09/09/2019 16:01, peteolcott wrote: > All infinities are the same size. Nonsense. Infinity doesn't have a size by definition. /Flibble -- “You won’t burn in hell. But be nice anyway.” – Ricky Gervais “I see Atheists are fighting and killing each other again, over who doesn’t believe in any God the most. Oh, no..wait.. that never happens.” – Ricky Gervais "Suppose it's all true, and you walk up to the pearly gates, and are confronted by God," Bryne asked on his show The Meaning of Life. "What will Stephen Fry say to him, her, or it?" "I'd say, bone cancer in children? What's that about?" Fry replied. "How dare you? How dare you create a world to which there is such misery that is not our fault. It's not right, it's utterly, utterly evil." "Why should I respect a capricious, mean-minded, stupid God who creates a world that is so full of injustice and pain. That's what I would say."
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-09 18:05 -0500 |
| Message-ID | <MfCdnXtPEYlXR-vAnZ2dnUU7-UnNnZ2d@giganews.com> |
| In reply to | #19091 |
On 9/9/2019 3:38 PM, Mr Flibble wrote: > On 09/09/2019 16:01, peteolcott wrote: >> All infinities are the same size. > > Nonsense. Infinity doesn't have a size by definition. > > /Flibble > Congratulations your answer is more precisely accurate than mine. I did not provide the more precise answer because it would have been to much for the target audience to handle. So Cantor was not just wrong about differing cardinality he was dead wrong. One can count all of the (otherwise uncountable) real numbers by merely counting all of the adjacent geometric points on a number line. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2019-09-10 09:01 +0200 |
| Message-ID | <ql7hnn$52u$1@dont-email.me> |
| In reply to | #19089 |
On 09/09/2019 17:01, peteolcott wrote: > > https://en.wikipedia.org/wiki/Continuum_hypothesis > It turns out that the basis concept of cardinality is ill-formed. No, it is not. Cardinality is a mathematical concept with a mathematical definition. It turns out that we can do useful and interesting things depending on certain extra features that we can choose to define, or not to define, but that does not make the definition ill-formed in any sense. > All infinities are the same size. Absolute drivel. > > The number of real numbers is the number of adjacent geometric > points on a number line, countable using integers. > The cardinality of the set of real numbers is /easily/ shown to be bigger than the cardinality of the integers (countable infinity). (Well, /easily/ if you know that kind of mathematics.) Since you posted a link to the Wikipedia article on the Continuum Hypothesis, did you actually attempt to read it? The second line sums up the hypothesis: """ There is no set whose cardinality is strictly between that of the integers and the real numbers. """ The implication from this is that you have at least two different sizes of infinity, the cardinality of integers (aleph_0) and the cardinality of real numbers (2 ^ aleph_0). Whether you accept the continuum hypothesis or not, you can't get past that sentence and still think those two cardinalities are the same size.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-10 10:38 -0500 |
| Message-ID | <pMqdnQFBSMfCXurAnZ2dnUU7-d3NnZ2d@giganews.com> |
| In reply to | #19094 |
On 9/10/2019 2:01 AM, David Brown wrote: > On 09/09/2019 17:01, peteolcott wrote: > >> >> https://en.wikipedia.org/wiki/Continuum_hypothesis >> It turns out that the basis concept of cardinality is ill-formed. > > No, it is not. Cardinality is a mathematical concept with a > mathematical definition. It turns out that we can do useful and > interesting things depending on certain extra features that we can > choose to define, or not to define, but that does not make the > definition ill-formed in any sense. > >> All infinities are the same size. > > Absolute drivel. > >> >> The number of real numbers is the number of adjacent geometric >> points on a number line, countable using integers. >> > > The cardinality of the set of real numbers is /easily/ shown to be > bigger than the cardinality of the integers (countable infinity). > (Well, /easily/ if you know that kind of mathematics.) > Yes I am aware of diagonal argument. You did not pay attention that I just refuted this: >> The number of real numbers is the number of adjacent geometric >> points on a number line, countable using integers. The next real number after 3.0 is the geometric point on the number line that is immediately adjacent to 3.0 on its right side. This geometric point is an infinitesimally larger than 3.0: encoded as the first point in the interval: (3,4] https://en.wikipedia.org/wiki/Bracket_(mathematics) > Since you posted a link to the Wikipedia article on the Continuum > Hypothesis, did you actually attempt to read it? The second line sums > up the hypothesis: If the concept of cardinality is bogus, then any theorem based on a bogus concept is also bogus. > > """ > There is no set whose cardinality is strictly between that of the > integers and the real numbers. > """ > > The implication from this is that you have at least two different sizes > of infinity, the cardinality of integers (aleph_0) and the cardinality > of real numbers (2 ^ aleph_0). Whether you accept the continuum > hypothesis or not, you can't get past that sentence and still think > those two cardinalities are the same size. > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2019-09-10 22:01 +0200 |
| Message-ID | <ql8ven$lt9$1@dont-email.me> |
| In reply to | #19096 |
I have removed comp.lang.c++ from the list of newsgroups here, as this has absolutely nothing to do with C++. I have no idea if it is relevant to any of the other groups you have cross-posted to - I'd be surprised. I don't read those groups, and won't see any follow-ups there. I have tried to answer you below. If you are interested in the mathematics, and are willing to read a little, think a lot, and learn more mathematics, then you can reply to me by email. But please do so only if you want to get a better understanding of infinities - and a better understanding of your own limitations. On 10/09/2019 17:38, peteolcott wrote: > On 9/10/2019 2:01 AM, David Brown wrote: >> On 09/09/2019 17:01, peteolcott wrote: >> >>> >>> https://en.wikipedia.org/wiki/Continuum_hypothesis >>> It turns out that the basis concept of cardinality is ill-formed. >> >> No, it is not. Cardinality is a mathematical concept with a >> mathematical definition. It turns out that we can do useful and >> interesting things depending on certain extra features that we can >> choose to define, or not to define, but that does not make the >> definition ill-formed in any sense. >> >>> All infinities are the same size. >> >> Absolute drivel. >> >>> >>> The number of real numbers is the number of adjacent geometric >>> points on a number line, countable using integers. >>> >> >> The cardinality of the set of real numbers is /easily/ shown to be >> bigger than the cardinality of the integers (countable infinity). >> (Well, /easily/ if you know that kind of mathematics.) >> > > Yes I am aware of diagonal argument. The "diagonal argument" that could be relevant here is used to show that the size of the set of rational numbers is the same as the size of the set of integers. It is not relevant to the real numbers. > You did not pay attention that I just refuted this: 1. I did not see any such post. 2. It is wrong anyway. > > >> The number of real numbers is the number of adjacent geometric > >> points on a number line, countable using integers. > > The next real number after 3.0 is the geometric point on the number > line that is immediately adjacent to 3.0 on its right side. This geometric > point is an infinitesimally larger than 3.0: encoded as the first point in > the interval: (3,4] Incorrect. There is no "point adjacent to 3.0 on its right side". Here is a very simple proof of that, by reductio ad absurdum : 1. Assume there is such a real number, and call it "x". 2. Let "y" be "(3.0 + x) / 2". The reals are a field, so this is another real number. 3. We know that "x" is strictly greater than 3.0, by its definition. So "3.0 + x" is strictly greater than "3.0 + 3.0". Thus "y" is strictly greater than 3.0. Similarly, "y" is strictly less than "x". 4. So "y" is a real number to the right of 3.0, but to the left of "x". This contradicts the definition of "x". > > https://en.wikipedia.org/wiki/Bracket_(mathematics) > > >> Since you posted a link to the Wikipedia article on the Continuum >> Hypothesis, did you actually attempt to read it? The second line sums >> up the hypothesis: > > If the concept of cardinality is bogus, then any theorem based on > a bogus concept is also bogus. > That statement is logically correct, but unhelpful. The cardinality (whether you mean the concept of "cardinality", or the statements I have made about infinite cardinalities) is not bogus. And the Continuum Hypothesis is not based on any particular cardinalities, in that both the CH and its negation are consistent with the cardinality of the reals being strictly bigger than the cardinality of the integers. >> >> """ >> There is no set whose cardinality is strictly between that of the >> integers and the real numbers. >> """ >> >> The implication from this is that you have at least two different sizes >> of infinity, the cardinality of integers (aleph_0) and the cardinality >> of real numbers (2 ^ aleph_0). Whether you accept the continuum >> hypothesis or not, you can't get past that sentence and still think >> those two cardinalities are the same size. >> > >
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-10 20:12 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness [ Infinitesimal numbers ] |
| Message-ID | <DO6dnaIqOqyT1-XAnZ2dnUU7-QnNnZ2d@giganews.com> |
| In reply to | #19097 |
On 9/10/2019 3:01 PM, David Brown wrote: > I have removed comp.lang.c++ from the list of newsgroups here, as this has absolutely nothing to do with C++. I have no idea if it is relevant to any of the other groups you have cross-posted to - I'd be surprised. I don't read those groups, and won't see > any follow-ups there. > > I have tried to answer you below. If you are interested in the mathematics, and are willing to read a little, think a lot, and learn more mathematics, then you can reply to me by email. But please do so only if you want to get a better understanding of > infinities - and a better understanding of your own limitations. > > On 10/09/2019 17:38, peteolcott wrote: >> On 9/10/2019 2:01 AM, David Brown wrote: >>> On 09/09/2019 17:01, peteolcott wrote: >>> >>>> >>>> https://en.wikipedia.org/wiki/Continuum_hypothesis >>>> It turns out that the basis concept of cardinality is ill-formed. >>> >>> No, it is not. Cardinality is a mathematical concept with a >>> mathematical definition. It turns out that we can do useful and >>> interesting things depending on certain extra features that we can >>> choose to define, or not to define, but that does not make the >>> definition ill-formed in any sense. >>> >>>> All infinities are the same size. >>> >>> Absolute drivel. >>> >>>> >>>> The number of real numbers is the number of adjacent geometric >>>> points on a number line, countable using integers. >>>> >>> >>> The cardinality of the set of real numbers is /easily/ shown to be >>> bigger than the cardinality of the integers (countable infinity). >>> (Well, /easily/ if you know that kind of mathematics.) >>> >> >> Yes I am aware of diagonal argument. > > The "diagonal argument" that could be relevant here is used to show that the size of the set of rational numbers is the same as the size of the set of integers. It is not relevant to the real numbers. > >> You did not pay attention that I just refuted this: > > 1. I did not see any such post. > > 2. It is wrong anyway. > >> >> >> The number of real numbers is the number of adjacent geometric >> >> points on a number line, countable using integers. >> >> The next real number after 3.0 is the geometric point on the number >> line that is immediately adjacent to 3.0 on its right side. This geometric >> point is an infinitesimally larger than 3.0: encoded as the first point in >> the interval: (3,4] > > Incorrect. There is no "point adjacent to 3.0 on its right side". Here is a very simple proof of that, by reductio ad absurdum : > You made the fallacy of equivocation error when you change the term geometric point into real number. There is a geometric point that is greater than and adjacent to 3.0 3. followed by an infinite number of "0" followed by "1"---> 3.0∞1 3.0∞1 is indivisible because its Infinitesimal portion is indivisible. 3.0∞2 / 2.0 is 1.50∞1 3.0∞2 / 3.0 is indivisible It is already self-evident that ALL the geometric points on the number line is ALL the real numbers, thus the Infinitesimal number system counts ALL the reals. This is the brand new Infinitesimal number system. Copyright 2019 Pete Olcott > 1. Assume there is such a real number, and call it "x". > > 2. Let "y" be "(3.0 + x) / 2". The reals are a field, so this is another real number. > > 3. We know that "x" is strictly greater than 3.0, by its definition. So "3.0 + x" is strictly greater than "3.0 + 3.0". Thus "y" is strictly greater than 3.0. Similarly, "y" is strictly less than "x". > > 4. So "y" is a real number to the right of 3.0, but to the left of "x". This contradicts the definition of "x". > >> >> https://en.wikipedia.org/wiki/Bracket_(mathematics) >> >> >>> Since you posted a link to the Wikipedia article on the Continuum >>> Hypothesis, did you actually attempt to read it? The second line sums >>> up the hypothesis: >> >> If the concept of cardinality is bogus, then any theorem based on >> a bogus concept is also bogus. >> > > That statement is logically correct, but unhelpful. The cardinality (whether you mean the concept of "cardinality", or the statements I have made about infinite cardinalities) is not bogus. And the Continuum Hypothesis is not based on any particular > cardinalities, in that both the CH and its negation are consistent with the cardinality of the reals being strictly bigger than the cardinality of the integers. > >>> >>> """ >>> There is no set whose cardinality is strictly between that of the >>> integers and the real numbers. >>> """ >>> >>> The implication from this is that you have at least two different sizes >>> of infinity, the cardinality of integers (aleph_0) and the cardinality >>> of real numbers (2 ^ aleph_0). Whether you accept the continuum >>> hypothesis or not, you can't get past that sentence and still think >>> those two cardinalities are the same size. >>> >> >> > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Reinhardt Behm <rbehm@hushmail.com> |
|---|---|
| Date | 2019-09-11 15:31 +0800 |
| Message-ID | <qla7sa$d23$1@dont-email.me> |
| In reply to | #19096 |
On 9/10/19 11:38 PM, peteolcott wrote: > The next real number after 3.0 is the geometric point on the number > line that is immediately adjacent to 3.0 on its right side. This geometric > point is an infinitesimally larger than 3.0: encoded as the first point in > the interval: (3,4] And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 12:04 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <er6dndJ1p8WItOTAnZ2dnUU7-d_NnZ2d@giganews.com> |
| In reply to | #19106 |
On 9/11/2019 2:31 AM, Reinhardt Behm wrote: > On 9/10/19 11:38 PM, peteolcott wrote: >> The next real number after 3.0 is the geometric point on the number >> line that is immediately adjacent to 3.0 on its right side. This geometric >> point is an infinitesimally larger than 3.0: encoded as the first point in >> the interval: (3,4] > > And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. > I specified a whole Infinitesimal number system: Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number of geometric points offset from the real part. 0.0[1,∞] specifies the entire set of geometric points with a value greater than zero on the number line which self-evidently corresponds to the entire set of positive reals. Notice that this entire set is countable using the set of positive integers. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Reinhardt Behm <rbehm@hushmail.com> |
|---|---|
| Date | 2019-09-12 10:20 +0800 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <qlca11$5fp$1@dont-email.me> |
| In reply to | #19110 |
On 9/12/19 1:04 AM, peteolcott wrote: > On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >> On 9/10/19 11:38 PM, peteolcott wrote: >>> The next real number after 3.0 is the geometric point on the number >>> line that is immediately adjacent to 3.0 on its right side. This >>> geometric >>> point is an infinitesimally larger than 3.0: encoded as the first >>> point in >>> the interval: (3,4] >> >> And between 3.0 and your "next" number (xnext) to the right is another >> real number: (3.0+xnext) / 2. >> > > > I specified a whole Infinitesimal number system: > Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number > of geometric points offset from the real part. > > 0.0[1,∞] specifies the entire set of geometric points with a value > greater than zero on the number line which self-evidently corresponds > to the entire set of positive reals. > > Notice that this entire set is countable using the set of positive > integers. If they are countable you can always list them in the counted order. With my above example I can always construct numbers that are not in your counted set. This disproves that you have counted them all. It disproves that they are countable at all.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 23:51 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <8bGdnYE-yO1FU-TAnZ2dnUU7-SXNnZ2d@giganews.com> |
| In reply to | #19119 |
On 9/11/2019 9:20 PM, Reinhardt Behm wrote: > On 9/12/19 1:04 AM, peteolcott wrote: >> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>> On 9/10/19 11:38 PM, peteolcott wrote: >>>> The next real number after 3.0 is the geometric point on the number >>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>> the interval: (3,4] >>> >>> And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. >>> >> >> >> I specified a whole Infinitesimal number system: >> Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number >> of geometric points offset from the real part. >> >> 0.0[1,∞] specifies the entire set of geometric points with a value >> greater than zero on the number line which self-evidently corresponds >> to the entire set of positive reals. >> >> Notice that this entire set is countable using the set of positive integers. > > If they are countable you can always list them in the counted order. With my above example I can always construct numbers that are not in your counted set. You can construct a number that is not on any point of the number line? In other words you can construct a number THAT IS NOT A NUMBER. That would be a (categorically impossible) neat trick. > This disproves that you have counted them all. It disproves that they are countable at all. > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Keith Thompson <kst-u@mib.org> |
|---|---|
| Date | 2019-09-12 01:22 -0700 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <lnwoedc4a0.fsf@kst-u.example.com> |
| In reply to | #19119 |
Reinhardt Behm <rbehm@hushmail.com> writes:
> On 9/12/19 1:04 AM, peteolcott wrote:
[...]
>> Notice that this entire set is countable using the set of positive
>> integers.
>
> If they are countable you can always list them in the counted order.
[...]
Reinhardt, let me urge you to take a look at comp.theory before
deciding whether it's worth your time to discuss anything with
Pete Olcott.
Either way, please drop comp.lang.c++ from the newsgroups list,
and consider whether the readers of comp.ai.philosophy want to read
about this.
--
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 | 2019-09-11 12:05 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <er6dnc11p8XwtOTAnZ2dnUU7-d9QAAAA@giganews.com> |
| In reply to | #19106 |
On 9/11/2019 2:31 AM, Reinhardt Behm wrote: > On 9/10/19 11:38 PM, peteolcott wrote: >> The next real number after 3.0 is the geometric point on the number >> line that is immediately adjacent to 3.0 on its right side. This geometric >> point is an infinitesimally larger than 3.0: encoded as the first point in >> the interval: (3,4] > > And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. > I specified a whole Infinitesimal number system: Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number of geometric points offset from the real part. 0.0[1,∞] specifies the entire set of geometric points with a value greater than zero on the number line which self-evidently corresponds to the entire set of positive reals. Notice that this entire set is countable using the set of positive integers. Copyright 2019 Pete Olcott -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 18:32 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <sqydnZDTcotlHuTAnZ2dnUU7-bXNnZ2d@giganews.com> |
| In reply to | #19111 |
On 9/11/2019 12:37 PM, Fred wrote: > On 11/09/2019 18:05, peteolcott wrote: >> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>> On 9/10/19 11:38 PM, peteolcott wrote: >>>> The next real number after 3.0 is the geometric point on the number >>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>> the interval: (3,4] >>> >>> And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. >>> >> >> I specified a whole Infinitesimal number system: >> Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number >> of geometric points offset from the real part. >> >> 0.0[1,∞] specifies the entire set of geometric points with a value >> greater than zero on the number line which self-evidently corresponds >> to the entire set of positive reals. >> >> Notice that this entire set is countable using the set of positive integers. > > If your "infinitesimal number system" contains the usual real numbers and some other things as well, it cannot have a smaller cardinality than just the usual real numbers on their own. > > My infinitesimal number system forms a bijection between the integers and all of the geometric points on a number line. We already know there is a bijection between all of the geometric points on a number line and the set of real numbers. Therefore the set of integers and the set of reals are the same size and Cantor was wrong about cardinality. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 20:03 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <18OdnXrmgfvKBOTAnZ2dnUU7-efNnZ2d@giganews.com> |
| In reply to | #19112 |
On 9/11/2019 7:42 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > <cut> >>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>>>> On 9/10/19 11:38 PM, peteolcott wrote: >>>>>> The next real number after 3.0 is the geometric point on the number >>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>>>> the interval: (3,4] > > There is no next real number after 3.0. There is not even a next rational > number after 3.0, and the rationals /are/ countable! I.e. you don't > need there to be a successor function on points that respects the > usual ordering of points to get a countable set between 3 and 4. As it > is, you open yourself up to the obvious problem: The line segment [3.0, 4.0) is exactly one geometric point longer than (3.0. 4.0). There is a geometric point immediately adjacent to 3.0 on the number line. This geometric point does correspond to a number because it is on the number line. Now I have to correct my prior reasoning. All of the geometric points on the number line correspond to all of the numbers that exist. Some of these are not real numbers. Since we can count all of these numbers with integers using the infinitesimal number system we have proven that the set of real numbers is not larger than the set of integers. Real_Part[Infinitesimal_Offset] 0.0[1 to ∞] forms a bijection between the positive integers and all of the positive numbers through all of the positive points on the number line. Copyright 2019 Pete Olcott > >>>>> And between 3.0 and your "next" number (xnext) to the right is >>>>> another real number: (3.0+xnext) / 2. > <cut> >> My infinitesimal number system forms a bijection between the integers and >> all of the geometric points on a number line. > > Ignoring questions won't make you right (but it will allow yo to keep > boasting). > > Talking of boasting, it's now nine months since you first claimed to > have an impossible "actual Turing machine" "fully encoded". No sign of > you ever posting it of course. > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 20:59 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <FtOdnVZus7sOO-TAnZ2dnUU7-e_NnZ2d@giganews.com> |
| In reply to | #19117 |
On 9/11/2019 8:50 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/11/2019 7:42 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>>>>>> On 9/10/19 11:38 PM, peteolcott wrote: >>>>>>>> The next real number after 3.0 is the geometric point on the number >>>>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>>>>>> the interval: (3,4] >>> >>> There is no next real number after 3.0. There is not even a next rational >>> number after 3.0, and the rationals /are/ countable! I.e. you don't >>> need there to be a successor function on points that respects the >>> usual ordering of points to get a countable set between 3 and 4. As it >>> is, you open yourself up to the obvious problem: >> >> The line segment [3.0, 4.0) is exactly one geometric point longer than >> (3.0. 4.0). > > I was going to say "correct!" because |[3, 4) \ (3, 4)| is indeed 1, but > that was before I saw that not all your PO-geometric points are real > numbers. Since I don't know what PO-geometric points really are I'll > just take your word for it. > >> There is a geometric point immediately adjacent to 3.0 on the number line. >> This geometric point does correspond to a number because it is on the >> number line. >> >> Now I have to correct my prior reasoning. All of the geometric points on >> the number line correspond to all of the numbers that exist. Some of these >> are not real numbers. >> >> Since we can count all of these numbers with integers using the infinitesimal >> number system > > You can not count all of these numbers with integers. You can not count > all of the reals let alone the PO-geometric points that (according to > you) includes things that are not real numbers. > >> we have proven that the set of real numbers is not larger >> than the set of integers. > > Saying "we can count..." is not a proof of counting. > >> Real_Part[Infinitesimal_Offset] >> >> 0.0[1 to ∞] forms a bijection between the positive integers and all of >> the positive numbers through all of the positive points on the number >> line. > > You can't mean that. Well, actually I know you might mean that, but > it's obviously wrong. I'll say why, but only if you agree to answer > questions about your claims in good faith -- you have to be prepared to > learn why you are wrong otherwise it's just a waste of both of our time. > (1) Do you understand that all of the points on a number line are all of the numbers? (2) Do you understand that a bijection between the integers and these points would make these points countable? -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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