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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 | 2019-09-19 17:31 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] |
| Message-ID | <d6udncuuBIQwnBnAnZ2dnUU7-a3NnZ2d@giganews.com> |
| In reply to | #19345 |
On 9/19/2019 4:44 PM, Keith Thompson wrote: > peteolcott <Here@Home> writes: > [SNIP] > > The phrase "Keith Thompson Concurrence" in the title of the parent > article is a lie. > That claim is proven to be counter-factual by the provided context. That I said you concur with me does not indicate that you totally agreed with every subtle nuance. The aspect that you did agree to forms the whole basis of my position: (1) Points on a number line immediately adjacent to each other can be conceived and differ by an infinitesimal value. On 9/16/2019 11:38 PM, Keith Thompson wrote: > I can imagine that *this* set has a least element. For example > we can define "iota" as an infinitesimal, something that is not a > real number but that has a location on the number line, directly > adjacent to the real number 0. It is greater than 0 and less than > any positive real number. (2) The intervals [A, B] - (A, B] = point: A. On 9/16/2019 5:46 PM, Keith Thompson wrote: > [A,B] is a set of real numbers. (A,B] can be constructed by taking > [A,B] and removing a single element, namely A, and similarily vice > versa. All members of (A,B] are members of [A,B], and there is > exactly one real number that is a member of [A,B] and not of (A,B]. From (1) and (2) the whole Infinitesimal number system is derived. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 11:02 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <RI2dnZdu_JSPL-LAnZ2dnUU7-I2dnZ2d@giganews.com> |
| In reply to | #19192 |
On 9/16/2019 10:26 AM, André G. Isaak wrote:
> On 2019-09-16 9:17 a.m., peteolcott wrote:
>> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>
>>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>>
>>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>>
>>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>>>> But this is a side issue.
>>>>>>>>
>>>>>>>> That is defining X = X + 1.
>>>>>>>
>>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>>> Making an open interval closed does no change the length.
>>>>>>
>>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>>> The first one is 0% to 100%
>>>>>> The second one is 0% to 99%
>>>>>
>>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>>
>>>> There are too many ways to correctly say this.
>>>> (0, 100] integers is 0 to 100
>>>> (0, 100) integers is 0 to 99
>>>
>>> No. Sadly, almost everything you post introduces new errors. There are
>>> no open intervals in the integers so using the () notation is silly.
>>>
>>> You can, of course, give it a meaning (as you have tried to do here) but
>>> even then you get it wrong. If the "open" end means the bound is
>>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>>
>>> Why switch to integers which have totally different properties?
>>>
>>>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>>>> (0, 1] a length of exactly 1.0
>>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>>
>>>>> It's not magic. Length is defined that way for a reason. As I have
>>>>> said time and time again, just call your notion PO-length, define it
>>>>> properly, and we can decide if we care about it or not.
>>>>>
>>>>
>>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>>> 0.0 to 100.0 not including the 100 is 0 to
>>>> 99.999999999999999999999999999999999999999... on to infinity
>>>
>>> I propose Ben's law: Every sufficiently long mathematical crank thread
>>> ends up "debating" whether 0.999... = 1 or not.
>>>
>>> No. 99.999... = 100 and you stated that 100 is not included.
>>>
>>> There is no notation for the largest real in the open interval (0, 100),
>>> not because no one has come up with a notation for it (that's trivial,
>>> but the words will do) but because there is no such number.
>>>
>>
>> Do you realize that you just said that the number line is defined with gaps?
>> There is either a contiguous set of points between 0 and 100 or there are
>> gaps between 0 and 100, those are the only two choices.
>
>
> No. You are describing a number line with gaps. He is not. If there were indeed some largest real in the interval (0,100) (let's call it L), then what number lies between L and 100? According to you, none. But, it is axiomatic that for the real numbers,
> for every x and every y if z < y then there exists some z such that x < z < y. This proves (by reductio ad absurdum) that there is no such number L.
>
> André
>
>
Since it is clear that (0,100) specifies every geometric point on the number
line between 0 and 100 except for 0 and 100 then it does specify the geometric
point immediately after 0 and the geometric point immediately before 100 with
no geometric points in-between.
If these geometric points are defined to be real numbers and real numbers
are defined to always be divisible by 2, then something about the way that
these things are defined is inherently inconsistent.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 20:01 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <DOedncdA-ZLFrR3AnZ2dnUU7-W_NnZ2d@giganews.com> |
| In reply to | #19190 |
On 9/16/2019 7:49 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/15/2019 6:33 AM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> 0.0 to 100.0 including the 100 is 0 to 100.0 >>>> 0.0 to 100.0 not including the 100 is 0 to >>>> 99.999999999999999999999999999999999999999... on to infinity >>> >>> I propose Ben's law: Every sufficiently long mathematical crank thread >>> ends up "debating" whether 0.999... = 1 or not. >>> >>> No. 99.999... = 100 and you stated that 100 is not included. >>> >>> There is no notation for the largest real in the open interval (0, 100), >>> not because no one has come up with a notation for it (that's trivial, >>> but the words will do) but because there is no such number. >> >> Do you realize that you just said that the number line is defined with >> gaps? > > I realise I overestimated your reasoning powers and, frankly, I did > not think that possible given the low estimation I originally had. > >> There is either a contiguous set of points between 0 and 100 or there are >> gaps between 0 and 100, those are the only two choices. > > No, there are other options. The reals form a continuum, but contiguous > means touching or adjacent, and no two real are adjacent. Have you ever > considered getting an education? > >>> This fact follows trivially from the definition of an open set in a >>> metric space, or from the axioms of the reals, or from the first baby >>> steps in topology... Repeatedly referring to a provably non-existent >>> object is just silly. >> >> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >> An interval (open interval) is a set of points on a line lying between >> two fixed points A and B, where A and B themselves are considered not >> to belong to the interval. >> >> This means that there is a first point and there is a last point of every >> open interval. > > No it does not. Nothing on that page lets you conclude that. If you > knew what an open set was... Oh, sorry, that's me suggesting education > again. > >> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1]. > > Only if your points do not form a continuum. The real interval (0, 100) > does, and it has no first and no last number. [0, 100] has a first and last point and a first and last real number (0, 100) has a first and last point yet no first and last real number. When-so-ever we remove any portion from the front of the interval: [0, 100] It always has a first point. [0.5, 100] [0.1, 100] [0.0001, 100] [0.0000000000000001, 100] [0.000000000000...1, 100] (0, 100] -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 22:39 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <l8ydnWn97MjFyB3AnZ2dnUU7-fHNnZ2d@giganews.com> |
| In reply to | #19230 |
On 9/16/2019 9:25 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
> <cut>
>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
>>>
>>> Only if your points do not form a continuum. The real interval (0, 100)
>>> does, and it has no first and no last number.
>>
>> [0, 100] has a first and last point and a first and last real number
>
> Yes.
>
>> (0, 100) has a first and last point yet no first and last real number.
>
> No. For any real x in (0, 100) we can find smaller elements. In fact,
> infinitely many: xy for every y in (0, 1) is smaller than x.
There is a first point that cannot be identified with a real number.
It can ONLY be identified with the infinitesimal number: 0.0[1].
It only seems like there is no first point when trying to identify
this point with a real number.
>
>> When-so-ever we remove any portion from the front of the interval: [0, 100]
>> It always has a first point.
>
> No. It depends on whether the portion you remove is closed or only
> half-closed:
>
>> [0.5, 100]
>
> This results from removing [0, 0.5) and therefore does indeed have a
> least element. If you remove [0, 0.5] you get (0.5, 100] and, as you
> now know, that set does /not/ have a least element.
>
>> [0.1, 100]
>> [0.0001, 100]
>> [0.0000000000000001, 100]
>> [0.000000000000...1, 100]
>
> These, too, result from removing some half-open set.
>
>> (0, 100]
>
> This results from removing a closed set ({0}) and therefore does not
> have a least element.
>
> Don't you think you should pick a book about the real numbers now?
>
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 22:23 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <q_GdnekMsYSOPhzAnZ2dnUU7-fOdnZ2d@giganews.com> |
| In reply to | #19234 |
On 9/17/2019 10:01 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/17/2019 8:26 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/16/2019 9:25 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/16/2019 7:49 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>> <cut>
>>>>>>>> (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
>>>>>>>
>>>>>>> Only if your points do not form a continuum. The real interval (0, 100)
>>>>>>> does, and it has no first and no last number.
>>>>>>
>>>>>> [0, 100] has a first and last point and a first and last real number
>>>>>
>>>>> Yes.
>>>>>
>>>>>> (0, 100) has a first and last point yet no first and last real number.
>>>>>
>>>>> No. For any real x in (0, 100) we can find smaller elements. In fact,
>>>>> infinitely many: xy for every y in (0, 1) is smaller than x.
>>>>
>>>> There is a first point that cannot be identified with a real number.
>>>> It can ONLY be identified with the infinitesimal number: 0.0[1].
>>>
>>> A notation you refused to explain when you saw the half-baked answers
>>> you gave to my initial questions were taking you into dangerous waters.
>>>
>>> You agree, it seems, that for the intervals everyone else cares about
>>> which are subsets or R, (0, 100) has no least element. Please confirm
>>> this. It matters. If you confirm it I can more on to ignoring
>>> PO-points and PO-intervals because no one cares about them until you
>>> can define.
>
> Are you really try to avoid confirming this, or have you just stopped
> reading what people write?
>
The conversation has moved way past this. Now my point is built
on the basis of Mike and Keith's agreement.
I SUMMED IT UP MORE CONCISELY HERE:
THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
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
On 9/16/2019 8:33 PM, Mike Terry wrote:
> OK, so (A,B] = [A,B] - {A}, and that can be counted as an "operation
in which we get (A,B] from [A,B].
Mike Terry agreed with this verbatim: [A, B] - {A} = (A, B]
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
--
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 | 2019-09-18 01:39 -0700 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <lnv9tq6lru.fsf@kst-u.example.com> |
| In reply to | #19278 |
peteolcott <Here@Home> writes:
[...]
> The conversation has moved way past this. Now my point is built
> on the basis of Mike and Keith's agreement.
Stop using my name to support your claims.
--
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 | 2019-09-18 09:59 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <PYKdnZn3lqXG2x_AnZ2dnUU7-IWdnZ2d@giganews.com> |
| In reply to | #19291 |
On 9/18/2019 3:39 AM, Keith Thompson wrote: > peteolcott <Here@Home> writes: > [...] >> The conversation has moved way past this. Now my point is built >> on the basis of Mike and Keith's agreement. > > Stop using my name to support your claims. > HELL NO !!! THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 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 | 2019-09-18 09:21 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qlti2i$vm4$1@dont-email.me> |
| In reply to | #19292 |
On 2019-09-18 8:59 a.m., peteolcott wrote: > On 9/18/2019 3:39 AM, Keith Thompson wrote: >> peteolcott <Here@Home> writes: >> [...] >>> The conversation has moved way past this. Now my point is built >>> on the basis of Mike and Keith's agreement. >> >> Stop using my name to support your claims. >> > > HELL NO !!! > > THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 > 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. > This paragraph that you keep quoting was followed by additional material which you conveniently ignore. That material made it quite clear that he was *not* supporting your view. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 10:41 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <K--dnQ3jksihzR_AnZ2dnUU7-QWdnZ2d@giganews.com> |
| In reply to | #19295 |
On 9/18/2019 10:21 AM, André G. Isaak wrote: > On 2019-09-18 8:59 a.m., peteolcott wrote: >> On 9/18/2019 3:39 AM, Keith Thompson wrote: >>> peteolcott <Here@Home> writes: >>> [...] >>>> The conversation has moved way past this. Now my point is built >>>> on the basis of Mike and Keith's agreement. >>> >>> Stop using my name to support your claims. >>> >> >> HELL NO !!! >> >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> 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. >> > > This paragraph that you keep quoting was followed by additional material which you conveniently ignore. That material made it quite clear that he was *not* supporting your view. > > André > Bullshit -- 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 | 2019-09-18 13:55 -0700 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <lnimpp72a2.fsf@kst-u.example.com> |
| In reply to | #19297 |
peteolcott <Here@Home> writes:
> On 9/18/2019 10:21 AM, André G. Isaak wrote:
>> On 2019-09-18 8:59 a.m., peteolcott wrote:
>>> On 9/18/2019 3:39 AM, Keith Thompson wrote:
>>>> peteolcott <Here@Home> writes:
>>>> [...]
>>>>> The conversation has moved way past this. Now my point is built
>>>>> on the basis of Mike and Keith's agreement.
>>>>
>>>> Stop using my name to support your claims.
>>>>
>>>
>>> HELL NO !!!
>>>
>>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
>>> 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.
>>>
>>
>> This paragraph that you keep quoting was followed by additional
>> material which you conveniently ignore. That material made it quite
>> clear that he was *not* supporting your view.
>>
>> André
>>
>
> Bullshit
This paragraph that you keep quoting was followed by additional
material which you conveniently ignore. That material made it quite
clear that I was not supporting your view.
I do not expect to convince you of anything, nor am I interested in
doing so, but I expect these two paragraphs will appear with multiple
preceding ">" characters in multiple followups (unless you snip them)
The open interval (0,1] over the real numbers has no least element
(you have recently claimed that it does). An open interval (0,1]
over some proper superset of the real numbers could conceivably have
a least element, but I don't believe it could do so unless that set
is deliberately constructed to make this claim true, which is not a
useful thing to do (I'm less than 100% confident of this statement).
The cardinality of the reals is greater than the cardinality of the
integers. The cardinality of any superset of the reals is greater
than the cardinality of the integers. All these statements are in
direct disagreement with claims you have made here.
Given your habit of quoting the entirety of the parent article in
each followup, I expect you'll continue to cite me in support of
your claims while quoting this article in which I clearly state that
I disagree with you. I've asked you not to cite me in support of
your claims, and I ask you again now to stop, but I do not anticipate
that you will respect that simple request.
--
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 | 2019-09-18 16:17 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <AuidnQfeiZ5KAx_AnZ2dnUU7-afNnZ2d@giganews.com> |
| In reply to | #19313 |
On 9/18/2019 3:55 PM, Keith Thompson wrote: > peteolcott <Here@Home> writes: >> On 9/18/2019 10:21 AM, André G. Isaak wrote: >>> On 2019-09-18 8:59 a.m., peteolcott wrote: >>>> On 9/18/2019 3:39 AM, Keith Thompson wrote: >>>>> peteolcott <Here@Home> writes: >>>>> [...] >>>>>> The conversation has moved way past this. Now my point is built >>>>>> on the basis of Mike and Keith's agreement. >>>>> >>>>> Stop using my name to support your claims. >>>>> >>>> >>>> HELL NO !!! >>>> >>>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >>>> 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. >>>> >>> >>> This paragraph that you keep quoting was followed by additional >>> material which you conveniently ignore. That material made it quite >>> clear that he was *not* supporting your view. >>> >>> André >>> >> >> Bullshit > > This paragraph that you keep quoting was followed by additional > material which you conveniently ignore. That material made it quite > clear that I was not supporting your view. > > I do not expect to convince you of anything, nor am I interested in > doing so, but I expect these two paragraphs will appear with multiple > preceding ">" characters in multiple followups (unless you snip them) > > The open interval (0,1] over the real numbers has no least element > (you have recently claimed that it does). An open interval (0,1] > over some proper superset of the real numbers could conceivably have > a least element, but I don't believe it could do so unless that set > is deliberately constructed to make this claim true, which is not a > useful thing to do (I'm less than 100% confident of this statement). > The cardinality of the reals is greater than the cardinality of the > integers. The cardinality of any superset of the reals is greater > than the cardinality of the integers. All these statements are in > direct disagreement with claims you have made here. > Integer N = 0; HERE: N = N + 1; goto HERE; Since infinity is a process rather that a value it is impossible for any infinite sets to have a differing "size". Within the concept of the Infinitesimal Number system Reals are a subset and Integers form an index thus a bijection to Infinitesimals. We know that there is no Real number that is immediately adjacent to 0.0, thus we know that there is always a measurable gap between 0.0 and the next closest Real number, ONLY Infinitesimals totally fill this gap. > Given your habit of quoting the entirety of the parent article in > each followup, I expect you'll continue to cite me in support of > your claims while quoting this article in which I clearly state that > I disagree with you. I've asked you not to cite me in support of > your claims, and I ask you again now to stop, but I do not anticipate > that you will respect that simple request. > YOU CLEARLY STATE THAT YOU AGREE WITH ME IN THIS FULL CONTEXT THUS ANYTHING THAT YOU SAY THAT CONTRADICTS THIS AGREEMENT IS COUNTER-FACTUAL: On 9/16/2019 11:38 PM, Keith Thompson wrote:> > Thanks for the clarification. > > Here's my attempt to refute the idea that (A,B] has a least element. > I'm not trying to argue with Pete (though I expect he'll see this and > respond to it). > > Briefly, if (0,1] has a least member, what about the result of dividing > that member by 2? > > In more detail, (0,1] is the half-open interval consisting of > the real numbers between 0 and 1, including 1 but excluding 0. > Assume that this interval has a least element, an element x such > that for each member m of the interval, either x<m or x=m. > > Let y=x/2. If we're dealing with real numbers, then 0<y<x, and y > is a member of the interval and is less than x -- contradicting > the original assertion that x is the least element. Conclusion: > the interval (a set of real numbers) has no least element. THE ABOVE REFUTED (A, B] HAS A LEAST REAL ELEMENT. THE SECOND PARAGRAPH OF THIS AFFIRMS THAT A NUMBER IMMEDIATELY ADJACENT TO 0.0 COULD BE CONCEIVED. > Arbitrarily inventing a new notation, let _(0,1]_ be a set of, um, > something or other. It includes all the real numbers in (0,1], > and it may also include some other things, each of which is greater > than 0, less than or equal to 1, and somewhere on the "number line" > between 0 and 1. Some of the non-real elements might be points, > or infinitesimals. I'll assert that for any two members of *this* > set, exactly one of a<b, a=b, a>b is true. > > I can imagine that *this* set has a least element. For example > we can define "iota" as an infinitesimal, something that is not a > real number but that has a location on the number line, directly > adjacent to the real number 0. It is greater than 0 and less than > any positive real number. > NONE OF THE FOLLOWING DISAVOWS THE ABOVE PARAGRAPH > For the same argument I used to demonstrate that x is not the least > member of the interval *not* to apply to iota, one of the following > must be true: > > - iota/2 <= 0 > - iota/2 >= iota > - iota/2 is not defined > > Though we can define something like this, I'm having difficulty > thinking of a way to define it that is consistent *and useful*. > We need the non-real members of the interval to behave radically > differently under common arithmetic operations. Not that there's > anything wrong with that, but it seems to require inventing a set > that's even denser than the reals, but is nevertheless in some > vague sense discrete rather than continuous. As far as I can tell > (and it's very likely I've missed something), most proposed systems > of infinitesimals do not have this property. > -- 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 | 2019-09-18 11:10 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- [ CONCURRENCE ] |
| Message-ID | <zPOdnf1xsIOfyh_AnZ2dnUU7-SPNnZ2d@giganews.com> |
| In reply to | #19295 |
On 9/18/2019 10:21 AM, André G. Isaak wrote: > On 2019-09-18 8:59 a.m., peteolcott wrote: >> On 9/18/2019 3:39 AM, Keith Thompson wrote: >>> peteolcott <Here@Home> writes: >>> [...] >>>> The conversation has moved way past this. Now my point is built >>>> on the basis of Mike and Keith's agreement. >>> >>> Stop using my name to support your claims. >>> >> >> HELL NO !!! >> >> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0 >> 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. >> > > This paragraph that you keep quoting was followed by additional material which you conveniently ignore. That material made it quite clear that he was *not* supporting your view. > > André > HERE IS THE RELEVANT CONTEXT PROVING THAT THIS CONTEXT DOES NOT IN ANY WAY DISAVOW THE QUOTED PARAGRAPH, AND THAT SUBSEQUENT CLAIMS THAT HE DID NOT SUPPORT MY VIEW ARE PROVEN TO BE COUNTER-FACTUAL. On 9/16/2019 11:38 PM, Keith Thompson wrote: > Arbitrarily inventing a new notation, let _(0,1]_ be a set of, um, > something or other. It includes all the real numbers in (0,1], > and it may also include some other things, each of which is greater > than 0, less than or equal to 1, and somewhere on the "number line" > between 0 and 1. Some of the non-real elements might be points, > or infinitesimals. I'll assert that for any two members of *this* > set, exactly one of a<b, a=b, a>b is true. > > I can imagine that *this* set has a least element. For example > we can define "iota" as an infinitesimal, something that is not a > real number but that has a location on the number line, directly > adjacent to the real number 0. It is greater than 0 and less than > any positive real number. > > For the same argument I used to demonstrate that x is not the least > member of the interval *not* to apply to iota, one of the following > must be true: > > - iota/2 <= 0 > - iota/2 >= iota > - iota/2 is not defined > > Though we can define something like this, I'm having difficulty > thinking of a way to define it that is consistent *and useful*. > We need the non-real members of the interval to behave radically > differently under common arithmetic operations. Not that there's > anything wrong with that, but it seems to require inventing a set > that's even denser than the reals, but is nevertheless in some > vague sense discrete rather than continuous. As far as I can tell > (and it's very likely I've missed something), most proposed systems > of infinitesimals do not have this property. > -- 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 | 2019-09-12 09:05 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qldmrj$675$1@dont-email.me> |
| In reply to | #19117 |
On 2019-09-11 7:03 p.m., peteolcott wrote: > 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). Assuming that X is the length of [3.0, 4.0) and y is the length of (3.0. 4.0), then what is (x-y)/2? What is 1/(x-y)? André > 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. >> > > > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-12 10:49 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <p_SdncZbpMti9efAnZ2dnUU7-R_NnZ2d@giganews.com> |
| In reply to | #19123 |
On 9/12/2019 10:05 AM, André G. Isaak wrote: > On 2019-09-11 7:03 p.m., peteolcott wrote: >> 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). > > Assuming that X is the length of [3.0, 4.0) and y is the length of (3.0. 4.0), then what is (x-y)/2? // singe geometric points are indivisible. What is 1/(x-y)? // I am not sure. I would have to think about it. This is basically 1.0 divided by infinitesimal. This may be disallowed too because it seems analogous to dividing by zero. > > André > >> 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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-12 10:02 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qldq7k$q3n$1@dont-email.me> |
| In reply to | #19126 |
On 2019-09-12 9:49 a.m., peteolcott wrote: > On 9/12/2019 10:05 AM, André G. Isaak wrote: >> On 2019-09-11 7:03 p.m., peteolcott wrote: >>> 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). >> >> Assuming that X is the length of [3.0, 4.0) and y is the length of >> (3.0. 4.0), then what is > (x-y)/2? // singe geometric points are indivisible. Then you're not talking about real numbers, are you? Do you understand what 'densely-ordered' means? André <snip> -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-13 00:18 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <NJWdnVj0vZwhu-bAnZ2dnUU7-QfNnZ2d@giganews.com> |
| In reply to | #19127 |
On 9/12/2019 11:02 AM, André G. Isaak wrote: > On 2019-09-12 9:49 a.m., peteolcott wrote: >> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>> On 2019-09-11 7:03 p.m., peteolcott wrote: >>>> 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). >>> >>> Assuming that X is the length of [3.0, 4.0) and y is the length of (3.0. 4.0), then what is >> (x-y)/2? // singe geometric points are indivisible. > > Then you're not talking about real numbers, are you? In some cases the only type of number corresponding to a point on a number line may not be any of the conventionally named numbers. That is why I call this the Infinitesimal number system. I was incorrectly initially thinking that all the numbers on a number line are real numbers. > > Do you understand what 'densely-ordered' means? > > André > > <snip> > > -- 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 | 2019-09-12 23:24 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlf97f$it$1@dont-email.me> |
| In reply to | #19144 |
On 2019-09-12 11:18 p.m., peteolcott wrote: > On 9/12/2019 11:02 AM, André G. Isaak wrote: >> On 2019-09-12 9:49 a.m., peteolcott wrote: >>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>> On 2019-09-11 7:03 p.m., peteolcott wrote: >>>>> 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). >>>> >>>> Assuming that X is the length of [3.0, 4.0) and y is the length of >>>> (3.0. 4.0), then what is >>> (x-y)/2? // singe geometric points are indivisible. >> >> Then you're not talking about real numbers, are you? > > In some cases the only type of number corresponding to a point on a number > line may not be any of the conventionally named numbers. > > That is why I call this the Infinitesimal number system. > I was incorrectly initially thinking that all the numbers > on a number line are real numbers. The following is one of the axioms which define the reals: If x < z, there exists a y such that x < y and y < z. If your "geometric points" are indivisible, then you are not describing the reals, since that would violate this axiom. André > >> >> Do you understand what 'densely-ordered' means? >> >> André >> >> <snip> >> >> > > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-13 10:01 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <_cWdnWHrEoivMubAnZ2dnUU7-c_NnZ2d@giganews.com> |
| In reply to | #19145 |
On 9/13/2019 12:24 AM, André G. Isaak wrote: > On 2019-09-12 11:18 p.m., peteolcott wrote: >> On 9/12/2019 11:02 AM, André G. Isaak wrote: >>> On 2019-09-12 9:49 a.m., peteolcott wrote: >>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>> On 2019-09-11 7:03 p.m., peteolcott wrote: >>>>>> 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). >>>>> >>>>> Assuming that X is the length of [3.0, 4.0) and y is the length of (3.0. 4.0), then what is >>>> (x-y)/2? // singe geometric points are indivisible. >>> >>> Then you're not talking about real numbers, are you? >> >> In some cases the only type of number corresponding to a point on a number >> line may not be any of the conventionally named numbers. >> >> That is why I call this the Infinitesimal number system. >> I was incorrectly initially thinking that all the numbers >> on a number line are real numbers. > > The following is one of the axioms which define the reals: > > If x < z, there exists a y such that x < y and y < z. > > If your "geometric points" are indivisible, then you are not describing the reals, since that would violate this axiom. > > André Yes I am not talking about reals. I am talking about infinitesimals. To the best of my knowledge I discovered the infinitesimal number system in 2018. A = (0.0, 1.0] B = (0,0, 1.0) Length(A) - Length(B) = C (one geometric point) C / 2.0 is undefined in the same way that 2.0 / 0.0 is undefined. -- 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 | 2019-09-13 09:13 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlgbn2$op0$1@dont-email.me> |
| In reply to | #19151 |
On 2019-09-13 9:01 a.m., peteolcott wrote: > On 9/13/2019 12:24 AM, André G. Isaak wrote: >> On 2019-09-12 11:18 p.m., peteolcott wrote: >>> On 9/12/2019 11:02 AM, André G. Isaak wrote: >>>> On 2019-09-12 9:49 a.m., peteolcott wrote: >>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>>> On 2019-09-11 7:03 p.m., peteolcott wrote: >>>>>>> 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). >>>>>> >>>>>> Assuming that X is the length of [3.0, 4.0) and y is the length of >>>>>> (3.0. 4.0), then what is >>>>> (x-y)/2? // singe geometric points are indivisible. >>>> >>>> Then you're not talking about real numbers, are you? >>> >>> In some cases the only type of number corresponding to a point on a >>> number >>> line may not be any of the conventionally named numbers. >>> >>> That is why I call this the Infinitesimal number system. >>> I was incorrectly initially thinking that all the numbers >>> on a number line are real numbers. >> >> The following is one of the axioms which define the reals: >> >> If x < z, there exists a y such that x < y and y < z. >> >> If your "geometric points" are indivisible, then you are not >> describing the reals, since that would violate this axiom. >> >> André > > Yes I am not talking about reals. I am talking about infinitesimals. > To the best of my knowledge I discovered the infinitesimal number system > in 2018. Then you shouldn't write things such as "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." > A = (0.0, 1.0] > B = (0,0, 1.0) > Length(A) - Length(B) = C (one geometric point) > C / 2.0 is undefined in the same way that 2.0 / 0.0 is undefined. So then how are multiplication and division defined in your system? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-13 09:56 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlge76$7ot$1@dont-email.me> |
| In reply to | #19152 |
On 2019-09-13 9:13 a.m., André G. Isaak wrote: > On 2019-09-13 9:01 a.m., peteolcott wrote: >> On 9/13/2019 12:24 AM, André G. Isaak wrote: >>> On 2019-09-12 11:18 p.m., peteolcott wrote: >>>> On 9/12/2019 11:02 AM, André G. Isaak wrote: >>>>> On 2019-09-12 9:49 a.m., peteolcott wrote: >>>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>>>> On 2019-09-11 7:03 p.m., peteolcott wrote: >>>>>>>> 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). >>>>>>> >>>>>>> Assuming that X is the length of [3.0, 4.0) and y is the length >>>>>>> of (3.0. 4.0), then what is >>>>>> (x-y)/2? // singe geometric points are indivisible. >>>>> >>>>> Then you're not talking about real numbers, are you? >>>> >>>> In some cases the only type of number corresponding to a point on a >>>> number >>>> line may not be any of the conventionally named numbers. >>>> >>>> That is why I call this the Infinitesimal number system. >>>> I was incorrectly initially thinking that all the numbers >>>> on a number line are real numbers. >>> >>> The following is one of the axioms which define the reals: >>> >>> If x < z, there exists a y such that x < y and y < z. >>> >>> If your "geometric points" are indivisible, then you are not >>> describing the reals, since that would violate this axiom. >>> >>> André >> >> Yes I am not talking about reals. I am talking about infinitesimals. >> To the best of my knowledge I discovered the infinitesimal number >> system in 2018. > > Then you shouldn't write things such as "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." > > >> A = (0.0, 1.0] >> B = (0,0, 1.0) >> Length(A) - Length(B) = C (one geometric point) >> C / 2.0 is undefined in the same way that 2.0 / 0.0 is undefined. > > So then how are multiplication and division defined in your system? Actually, let's ignore division for the moment and focus only on addition and multiplication. Using your R[I] notation where R is the 'real' part and I is the 'infinitesimal part', how does one go about solving the following: a[x] + b[y] = ? a[x] • b[y] = ? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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