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Groups > sci.math > #457916 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-09-11 12:05 -0500 |
| Last post | 2019-09-16 22:17 -0700 |
| Articles | 20 on this page of 169 — 9 participants |
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Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 12:05 -0500
Re: Provably unprovable eliminates incompleteness (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> - 2019-09-13 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 14:41 -0500
Re: Cantor was wrong about cardinality --- APOLOGY André G. Isaak <agisaak@gm.invalid> - 2019-09-14 14:08 -0600
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 15:45 -0500
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:06 -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> - 2019-09-14 22:40 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:40 -0600
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? 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 Transfinite Numbers <bursejan@gmail.com> - 2019-09-16 12:30 -0700
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). Zelos Malum <zelos.malum@gmail.com> - 2019-09-17 00:22 -0700
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 (some concurrence). Zelos Malum <zelos.malum@gmail.com> - 2019-09-17 22:23 -0700
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 (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) peteolcott <Here@Home> - 2019-09-13 13:03 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 12:34 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 16:38 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:00 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-14 00:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-17 11:33 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:25 -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 (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 22:43 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-16 23:12 -0600
Re: Provably unprovable eliminates incompleteness (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) Eram semper recta <thenewcalculus@gmail.com> - 2019-09-19 09:00 -0700
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 11:42 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Eram semper recta <thenewcalculus@gmail.com> - 2019-09-19 10:04 -0700
Re: Provably unprovable eliminates incompleteness (NO GAPS) Eram semper recta <thenewcalculus@gmail.com> - 2019-09-19 10:14 -0700
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 12:43 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Eram semper recta <thenewcalculus@gmail.com> - 2019-09-19 15:03 -0700
Re: Provably unprovable eliminates incompleteness (NO GAPS) Zelos Malum <zelos.malum@gmail.com> - 2019-09-18 22:16 -0700
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 (cardinality is incorrect) Zelos Malum <zelos.malum@gmail.com> - 2019-09-11 22:23 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-12 01:07 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Zelos Malum <zelos.malum@gmail.com> - 2019-09-12 22:24 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-13 00:34 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Zelos Malum <zelos.malum@gmail.com> - 2019-09-15 22:31 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-16 09:55 -0500
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) Zelos Malum <zelos.malum@gmail.com> - 2019-09-16 22:17 -0700
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 09:42 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) |
| Message-ID | <7qSdnSU8DrbBAuLAnZ2dnUU7-XHNnZ2d@giganews.com> |
| In reply to | #458283 |
On 9/16/2019 5:52 AM, Andy Walker wrote: > On 15/09/2019 00:00, peteolcott wrote: >>>> It is self evident that there is a bijection between the set of >>>> points on a number line and the set of all numbers. >>> No, that is not self-evident, and it is not even true for >>> some definitions of "number". >> If there is a number that is not on the number line that is >> like a non existent thing that exists even though it does >> not exist. > > [I realise that there is no helping PO, but others may > find some of what follows interesting.] > > It would help if you understood what a number is; but > you don't. Or what a line is; but you don't. Or bijections, > proofs, .... You are in the position of a barrack-room lawyer > who thinks the law operates entirely by common sense, dismisses > all the subtleties as "extraneous detail", and, worse, refuses > even to acknowledge that other countries may have different laws > from the ones he thinks are "self-evident". Or of a preacher > who believes not only that his religion is the One True way -- > all religions do that -- but that no other religion even exists. > > There is a reason why the quite simple things that > Cantor, Godel, Turing, ... discuss weren't discovered hundreds > of years earlier. For several centuries, the new discoveries > of modern-ish algebra, co-ordinate geometry, logarithms and > exponentials, calculus, differential equations, complex numbers, > and much else besides kept mathematicians, and scientists more > generally, busy without worrying too much about rigour. Only > when the cracks -- the "extraneous detail" -- started to appear > did people go back to basics, to discover that what was "self- > evident" to some was not so obvious to others, and in many > cases wasn't even true. Lots of new mathematics came out of > the drive to get the foundations right. > > It was filling in those cracks that made people think > more carefully about the limitations of the way maths/science > had developed. There is no longer One True Mathematics [though > some fundamentalists still affect to believe so]. There are > different sorts of number, different sorts of logic, different > computers, quantum mechanics, ..., no one more or less valid > than the others, and none of them guaranteed to be the version > adopted by intelligent life elsewhere in the Universe. > It seems like entirely rhetoric utterly bereft of any reasoning that addresses the point unless we consider the reference to complex numbers as tangentially addressing the point. Every number that exists is on the number line. Make pretend numbers that don't actually exist are not on the 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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-16 09:13 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE (Andy really did Goof) |
| Message-ID | <qlo8qo$db7$1@dont-email.me> |
| In reply to | #458426 |
On 2019-09-16 8:42 a.m., peteolcott wrote: > On 9/16/2019 5:52 AM, Andy Walker wrote: >> On 15/09/2019 00:00, peteolcott wrote: >>>>> It is self evident that there is a bijection between the set of >>>>> points on a number line and the set of all numbers. >>>> No, that is not self-evident, and it is not even true for >>>> some definitions of "number". >>> If there is a number that is not on the number line that is >>> like a non existent thing that exists even though it does >>> not exist. >> >> [I realise that there is no helping PO, but others may >> find some of what follows interesting.] >> >> It would help if you understood what a number is; but >> you don't. Or what a line is; but you don't. Or bijections, >> proofs, .... You are in the position of a barrack-room lawyer >> who thinks the law operates entirely by common sense, dismisses >> all the subtleties as "extraneous detail", and, worse, refuses >> even to acknowledge that other countries may have different laws >> from the ones he thinks are "self-evident". Or of a preacher >> who believes not only that his religion is the One True way -- >> all religions do that -- but that no other religion even exists. >> >> There is a reason why the quite simple things that >> Cantor, Godel, Turing, ... discuss weren't discovered hundreds >> of years earlier. For several centuries, the new discoveries >> of modern-ish algebra, co-ordinate geometry, logarithms and >> exponentials, calculus, differential equations, complex numbers, >> and much else besides kept mathematicians, and scientists more >> generally, busy without worrying too much about rigour. Only >> when the cracks -- the "extraneous detail" -- started to appear >> did people go back to basics, to discover that what was "self- >> evident" to some was not so obvious to others, and in many >> cases wasn't even true. Lots of new mathematics came out of >> the drive to get the foundations right. >> >> It was filling in those cracks that made people think >> more carefully about the limitations of the way maths/science >> had developed. There is no longer One True Mathematics [though >> some fundamentalists still affect to believe so]. There are >> different sorts of number, different sorts of logic, different >> computers, quantum mechanics, ..., no one more or less valid >> than the others, and none of them guaranteed to be the version >> adopted by intelligent life elsewhere in the Universe. >> > > It seems like entirely rhetoric utterly bereft of any reasoning > that addresses the point unless we consider the reference to > complex numbers as tangentially addressing the point. > > Every number that exists is on the number line. Make pretend > numbers that don't actually exist are not on the number line. 'Make pretend numbers that don't actually exist' would include things like "the smallest real number greater than 3.0". André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 19:36 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE |
| Message-ID | <UMGdnQjjFNo5GuDAnZ2dnUU7-bfNnZ2d@giganews.com> |
| In reply to | #458150 |
On 9/14/2019 7:32 PM, peteolcott wrote:
> On 9/14/2019 7:26 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>> <cut>
>>> My ONLY point is that Cantor was wrong and all infinities are exactly the
>>> same "size" in that infinity doesn't actually have a size because it is
>>> not a number it is the process of {more}:
>>
>> Which only makes you wrong. Specifically about what you thought Cantor
>> was saying.
>>
>> Cantor's theorem states that, for every set S
>>
>> |S| < |P(S)|
>>
>> where P(S) denotes the power set of S and
>>
>> |X| < |Y|
>>
>> means that there is no surjective function from X to Y.
>>
>> In order to leverage people's intuition, it makes sense to describe |X|
>> as the size of X, but it's the existence of functions between sets that
>> actually matters.
>>
>> There is a bijection between R and P(N) so |R| = |P(N)| and hence |N| < |R|.
>>
>
> It does not matter what he said as long as the set of all numbers is countable
> with integers then the whole concept of
infinite sets with differing cardinality
> is refuted.
>
> https://en.wikipedia.org/wiki/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 | 2019-09-14 21:38 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE |
| Message-ID | <nMCdnSbim76POeDAnZ2dnUU7-XXNnZ2d@giganews.com> |
| In reply to | #458286 |
On 9/14/2019 8:54 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 7:32 PM, peteolcott wrote:
>>> On 9/14/2019 7:26 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>> <cut>
>>>>> My ONLY point is that Cantor was wrong and all infinities are exactly the
>>>>> same "size" in that infinity doesn't actually have a size because it is
>>>>> not a number it is the process of {more}:
>>>>
>>>> Which only makes you wrong. Specifically about what you thought Cantor
>>>> was saying.
>>>>
>>>> Cantor's theorem states that, for every set S
>>>>
>>>> |S| < |P(S)|
>>>>
>>>> where P(S) denotes the power set of S and
>>>>
>>>> |X| < |Y|
>>>>
>>>> means that there is no surjective function from X to Y.
>>>>
>>>> In order to leverage people's intuition, it makes sense to describe |X|
>>>> as the size of X, but it's the existence of functions between sets that
>>>> actually matters.
>>>>
>>>> There is a bijection between R and P(N) so |R| = |P(N)| and hence |N| < |R|.
>>>>
>>>
>>> It does not matter what he said as long as the set of all numbers is countable
>>> with integers then the whole concept of
>>
>> infinite sets with differing cardinality
>>
>>> is refuted.
>
> Provided "the set of all numbers" includes R as a subset, then what
> Cantor said does matter, because he proved that your "as long as..." is
> a counter factual.
>
If the set of ALL numbers can be counted using integers then
there is no such thing as infinities with differing cardinality
and whatever anyone ever said to the contrary is fully refuted
because a bijection between integers and numbers has been shown.
--
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 10:21 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE |
| Message-ID | <FqidnYOlOJIYNeLAnZ2dnUU7-dXNnZ2d@giganews.com> |
| In reply to | #458294 |
On 9/15/2019 6:53 AM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 10:14 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 8:54 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 7:32 PM, peteolcott wrote:
>>>>>>> On 9/14/2019 7:26 PM, Ben Bacarisse wrote:
>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>> <cut>
>>>>>>>>> My ONLY point is that Cantor was wrong and all infinities are exactly the
>>>>>>>>> same "size" in that infinity doesn't actually have a size because it is
>>>>>>>>> not a number it is the process of {more}:
>>>>>>>>
>>>>>>>> Which only makes you wrong. Specifically about what you thought Cantor
>>>>>>>> was saying.
>>>>>>>>
>>>>>>>> Cantor's theorem states that, for every set S
>>>>>>>>
>>>>>>>> |S| < |P(S)|
>>>>>>>>
>>>>>>>> where P(S) denotes the power set of S and
>>>>>>>>
>>>>>>>> |X| < |Y|
>>>>>>>>
>>>>>>>> means that there is no surjective function from X to Y.
>>>>>>>>
>>>>>>>> In order to leverage people's intuition, it makes sense to describe |X|
>>>>>>>> as the size of X, but it's the existence of functions between sets that
>>>>>>>> actually matters.
>>>>>>>>
>>>>>>>> There is a bijection between R and P(N) so |R| = |P(N)| and hence |N| < |R|.
>>>>>>>>
>>>>>>>
>>>>>>> It does not matter what he said as long as the set of all numbers is countable
>>>>>>> with integers then the whole concept of
>>>>>>
>>>>>> infinite sets with differing cardinality
>>>>>>
>>>>>>> is refuted.
>>>>>
>>>>> Provided "the set of all numbers" includes R as a subset, then what
>>>>> Cantor said does matter, because he proved that your "as long as..." is
>>>>> a counter factual.
>>>>
>>>> If the set of ALL numbers can be counted using integers then...
>>>
>>> ....anything goes. We all agree one that. However, they can't be, so
>>> don't worry.
>>
>> You have never agreed to that properly.
>> If anything goes then the square root of 5 is 17 and popsicles are
>> office buildings, so you don't really mean ANYTHING GOES.
>
> Anything goes /in the theory in question/, so yes, sqrt(5) = 17 is
> provable in a theory containing the contradiction you are claiming, but
> analysis (a deliberately vague term for the theory of real numbers) can
> not talk about popsicles or office buildings. Did I have to spell that
> out? Sorry, I'll try to remember that in future.
>
>>>> there is no such thing as infinities with differing cardinality
>>>> and whatever anyone ever said to the contrary is fully refuted
>>>> because a bijection between integers and numbers has been shown.
>>>
>>> Nope. You've been asked to give it by more optimistic people than I and
>>> of course there has been no such bijection presented. You think you've
>>> given one, but you are too arrogant to ask why we don't agree.
>
> But of course you still don't give the function that we know is
> impossible.
>
> Note that there are two matters here: I failed to say that anything goes
> in the theory being discussed rather than anything goes in the real
> world. And I point out that you have again not given the key function
> implied by your claim. Of the two, you comment only on the first. This
> makes it abundantly clear that you have no interest in an honest
> exchange of ideas. As long as people reply, you can convince your self
> that you are being taken seriously, and the screaming of lambs is dulled
> for a few moments.
>
It is self-evident based on the definitions of the meaning of the terms
that every geometric point on the number line corresponds to a single unique
real number and every real number corresponds to a single geometric point
on the number line, hence bijection.
--
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 | 2019-09-13 11:55 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <2aidnX8WNshkVObAnZ2dnUU7-dnNnZ2d@giganews.com> |
| In reply to | #458033 |
On 9/13/2019 10:45 AM, Fred wrote: > On 13/09/2019 06:10, peteolcott wrote: >> On 9/12/2019 11:04 AM, Fred wrote: >>> On 12/09/2019 16:49, peteolcott wrote: >>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>> >>> >>>>> 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. >>> >>> Oh dear. Your first post to sci.logic in this thread began "I specified a whole Infinitesimal number system:" But you didn't "specify" to such a degree that you can give an account of division? >>> >> >> Account for this division: x = 1.0 / 0.0 > > 1.0/0.0 is undefined (for reasons that I explained once and you called my post bizarre). > >> The same thing goes for dividing a single indivisible point. > > x = 1.0 / ??? > > in the case of your "single indivisible point" what should replace the ??? > z = Length([0.0, 1.0] - [0.0, 1.0)) x = 1.0 / z -- 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 | 2019-09-13 13:03 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <vtKdnbPQKNNLRObAnZ2dnUU7-fvNnZ2d@giganews.com> |
| In reply to | #458033 |
On 9/13/2019 12:14 PM, André G. Isaak wrote: > On 2019-09-13 10:36 a.m., peteolcott wrote: >> On 9/13/2019 10:41 AM, André G. Isaak wrote: >>> On 2019-09-13 9:09 a.m., peteolcott wrote: >>>> On 9/13/2019 12:16 AM, André G. Isaak wrote: >>>>> On 2019-09-12 11:10 p.m., peteolcott wrote: >>>>>> On 9/12/2019 11:04 AM, Fred wrote: >>>>>>> On 12/09/2019 16:49, peteolcott wrote: >>>>>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>>>> >>>>>>> >>>>>>>>> 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. >>>>>>> >>>>>>> Oh dear. Your first post to sci.logic in this thread began "I specified a whole Infinitesimal number system:" But you didn't "specify" to such a degree that you can give an account of division? >>>>>>> >>>>>> >>>>>> Account for this division: x = 1.0 / 0.0 >>>>>> The same thing goes for dividing a single indivisible point. >>>>> >>>>> So are you claiming that this indivisible point is equal to zero? >>>> >>>> NOT AT ALL. Where the Hell did you get the idea that infinitesimal = 0.0 ? >>> >>> Because you claimed that dividing by an infinitesimal would be analogous to dividing by zero. If your infinitesimal isn't equal to zero, then why would dividing by it be analogous to dividing by zero? >>> >> >> If you identify an single geometric point on a number line you >> already know that it is indivisible. > > I have no idea what that is supposed to mean. 4.0 would be a single geometric point on a number line and it is divisible. 10.0 would be a different single point on a number line and it is divisible. > >>> >>>>> If so, then [3.0, 4.0) and (3.0. 4.0) will have the *exact* same length. If your indivisible point is not equal to zero, then you should be able to tell us exactly how many of these indivisible points are present in each of the above intervals. >>> >>> So if you're going to ignore the above, let's try asking it in a different way. You claim numbers have a 'real' part and an 'infinitesimal part' where you express the infinitesimal part in brackets. So 1.0[1] is just slightly larger than 1.0. So >>> consider the equation >>> >>> 1.0[x] = 2.0[0] >>> >>> Solve for x. >>> >>> André >>> >>> >> >> There is a bijection between all of the geometric points on a number line and all of the numbers on a numbers line. > > What is the bijection? > > If you can actually express a bijection between your infinitesimals and the numbers on the number line you should be able to eliminate the real part from your theory altogether and just talk about the infinitesimal portion. > > So how does that work? > > André > Because infinity is a process rather than a number it does not work that way. It is obvious that all of the points on a number line correspond to all of the numbers and that all of the numbers correspond to all of the points, in this sense there is a bijection between numbers and points exists. Since infinitesimal numbers can be proven to exist on the basis of the difference in length of these two intervals: (0.0, 1.0] - (0.0. 1.0) creating a notational convention to uniquely identify infinitesimal numbers is logically justified. (0.0, ∞] specifies all of the points corresponding to all of the positive numbers. >> There is no bijection between all of the numbers on a number line and the real numbers on a number line. >> Your RHS is a real and the LHS is an infinitesimal there is no bijection for this. >> >> >> > > -- 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 12:34 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlgnfa$uvd$1@dont-email.me> |
| In reply to | #458165 |
On 2019-09-13 12:03 p.m., peteolcott wrote: > On 9/13/2019 12:14 PM, André G. Isaak wrote: >> On 2019-09-13 10:36 a.m., peteolcott wrote: >>> On 9/13/2019 10:41 AM, André G. Isaak wrote: >>>> On 2019-09-13 9:09 a.m., peteolcott wrote: >>>>> On 9/13/2019 12:16 AM, André G. Isaak wrote: >>>>>> On 2019-09-12 11:10 p.m., peteolcott wrote: >>>>>>> On 9/12/2019 11:04 AM, Fred wrote: >>>>>>>> On 12/09/2019 16:49, peteolcott wrote: >>>>>>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>>>>> >>>>>>>> >>>>>>>>>> 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. >>>>>>>> >>>>>>>> Oh dear. Your first post to sci.logic in this thread began "I >>>>>>>> specified a whole Infinitesimal number system:" But you didn't >>>>>>>> "specify" to such a degree that you can give an account of >>>>>>>> division? >>>>>>>> >>>>>>> >>>>>>> Account for this division: x = 1.0 / 0.0 >>>>>>> The same thing goes for dividing a single indivisible point. >>>>>> >>>>>> So are you claiming that this indivisible point is equal to zero? >>>>> >>>>> NOT AT ALL. Where the Hell did you get the idea that infinitesimal >>>>> = 0.0 ? >>>> >>>> Because you claimed that dividing by an infinitesimal would be >>>> analogous to dividing by zero. If your infinitesimal isn't equal to >>>> zero, then why would dividing by it be analogous to dividing by zero? >>>> >>> >>> If you identify an single geometric point on a number line you >>> already know that it is indivisible. >> >> I have no idea what that is supposed to mean. 4.0 would be a single >> geometric point on a number line and it is divisible. 10.0 would be a >> different single point on a number line and it is divisible. >> >>>> >>>>>> If so, then [3.0, 4.0) and (3.0. 4.0) will have the *exact* same >>>>>> length. If your indivisible point is not equal to zero, then you >>>>>> should be able to tell us exactly how many of these indivisible >>>>>> points are present in each of the above intervals. >>>> >>>> So if you're going to ignore the above, let's try asking it in a >>>> different way. You claim numbers have a 'real' part and an >>>> 'infinitesimal part' where you express the infinitesimal part in >>>> brackets. So 1.0[1] is just slightly larger than 1.0. So consider >>>> the equation >>>> >>>> 1.0[x] = 2.0[0] >>>> >>>> Solve for x. >>>> >>>> André >>>> >>>> >>> >>> There is a bijection between all of the geometric points on a number >>> line and all of the numbers on a numbers line. >> >> What is the bijection? >> >> If you can actually express a bijection between your infinitesimals >> and the numbers on the number line you should be able to eliminate the >> real part from your theory altogether and just talk about the >> infinitesimal portion. >> >> So how does that work? >> >> André >> > > Because infinity is a process rather than a number it does not work that > way. > > It is obvious that all of the points on a number line correspond to all > of the numbers > and that all of the numbers correspond to all of the points, in this > sense there is a > bijection between numbers and points exists. If it is so obvious then why not simply state the bijection? André > Since infinitesimal numbers can be proven to exist on the basis of the > difference in length of these two intervals: (0.0, 1.0] - (0.0. 1.0) The difference in length between those two intervals is exactly 0. I'd asked you previously whether you understood what a dense ordering was. You did not reply. I suggest you look it up. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 16:38 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <BLKdneelC-hdwODAnZ2dnUU7-UnNnZ2d@giganews.com> |
| In reply to | #458175 |
On 9/13/2019 1:34 PM, André G. Isaak wrote: > On 2019-09-13 12:03 p.m., peteolcott wrote: >> On 9/13/2019 12:14 PM, André G. Isaak wrote: >>> On 2019-09-13 10:36 a.m., peteolcott wrote: >>>> On 9/13/2019 10:41 AM, André G. Isaak wrote: >>>>> On 2019-09-13 9:09 a.m., peteolcott wrote: >>>>>> On 9/13/2019 12:16 AM, André G. Isaak wrote: >>>>>>> On 2019-09-12 11:10 p.m., peteolcott wrote: >>>>>>>> On 9/12/2019 11:04 AM, Fred wrote: >>>>>>>>> On 12/09/2019 16:49, peteolcott wrote: >>>>>>>>>> On 9/12/2019 10:05 AM, André G. Isaak wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>>>> 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. >>>>>>>>> >>>>>>>>> Oh dear. Your first post to sci.logic in this thread began "I specified a whole Infinitesimal number system:" But you didn't "specify" to such a degree that you can give an account of division? >>>>>>>>> >>>>>>>> >>>>>>>> Account for this division: x = 1.0 / 0.0 >>>>>>>> The same thing goes for dividing a single indivisible point. >>>>>>> >>>>>>> So are you claiming that this indivisible point is equal to zero? >>>>>> >>>>>> NOT AT ALL. Where the Hell did you get the idea that infinitesimal = 0.0 ? >>>>> >>>>> Because you claimed that dividing by an infinitesimal would be analogous to dividing by zero. If your infinitesimal isn't equal to zero, then why would dividing by it be analogous to dividing by zero? >>>>> >>>> >>>> If you identify an single geometric point on a number line you >>>> already know that it is indivisible. >>> >>> I have no idea what that is supposed to mean. 4.0 would be a single geometric point on a number line and it is divisible. 10.0 would be a different single point on a number line and it is divisible. >>> >>>>> >>>>>>> If so, then [3.0, 4.0) and (3.0. 4.0) will have the *exact* same length. If your indivisible point is not equal to zero, then you should be able to tell us exactly how many of these indivisible points are present in each of the above intervals. >>>>> >>>>> So if you're going to ignore the above, let's try asking it in a different way. You claim numbers have a 'real' part and an 'infinitesimal part' where you express the infinitesimal part in brackets. So 1.0[1] is just slightly larger than 1.0. So >>>>> consider the equation >>>>> >>>>> 1.0[x] = 2.0[0] >>>>> >>>>> Solve for x. >>>>> >>>>> André >>>>> >>>>> >>>> >>>> There is a bijection between all of the geometric points on a number line and all of the numbers on a numbers line. >>> >>> What is the bijection? >>> >>> If you can actually express a bijection between your infinitesimals and the numbers on the number line you should be able to eliminate the real part from your theory altogether and just talk about the infinitesimal portion. >>> >>> So how does that work? >>> >>> André >>> >> >> Because infinity is a process rather than a number it does not work that way. >> >> It is obvious that all of the points on a number line correspond to all of the numbers >> and that all of the numbers correspond to all of the points, in this sense there is a >> bijection between numbers and points exists. > > If it is so obvious then why not simply state the bijection? > > André > > >> Since infinitesimal numbers can be proven to exist on the basis of the >> difference in length of these two intervals: (0.0, 1.0] - (0.0. 1.0) > > The difference in length between those two intervals is exactly 0. > Even a universal consensus does not necessarily derive a truth as proven by the universal consensus that the Earth is flat prior to Pythagoras. Even the universal failure of "others" to agree that the width of a geometric point is infinitesimal rather than zero does not make them right and me wrong. If there is zero difference between the above to intervals then they are identical, since they are not identical then there is a non zero difference. The common knowledge received view of this is inconsistent, the infinitesimal number system view is not inconsistent therefore the former is incorrect and the latter is correct. -- 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 | 2019-09-14 22:00 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlkd0g$s93$1@dont-email.me> |
| In reply to | #458279 |
On 2019-09-14 3:38 p.m., peteolcott wrote: > On 9/13/2019 1:34 PM, André G. Isaak wrote: >> On 2019-09-13 12:03 p.m., peteolcott wrote: >>> Since infinitesimal numbers can be proven to exist on the basis >>> of the difference in length of these two intervals: (0.0, 1.0] - >>> (0.0. 1.0) >> >> The difference in length between those two intervals is exactly 0. >> > > Even a universal consensus does not necessarily derive a truth as > proven by the universal consensus that the Earth is flat prior to > Pythagoras. [Purely as an aside, you've made the above claim multiple times but never actually backed it up. The earliest *explicit* claim that the earth was spherical was likely due to Parmenides, but we have no explicit denials that the earth was a sphere prior to that, so we really don't know what everyone believed.] > Even the universal failure of "others" to agree that the width of a > geometric point is infinitesimal rather than zero does not make them > right and me wrong. Either infinitesimal = zero or it does not. If it does not, then the length of any finite interval should be finite. So what are the exact lengths of (0.0, 1.0] and (0.0, 1.0) expressed as infinitesimals? Also, claiming that (0.0, 1.0] - (0.0. 1.0) = 1 infinitesimal (by which I assume you mean (0.0[0], 1.0[0]] - (0.0[0], 1.0[0]) = 0.0[1] in your number system since that's what we are talking about and you claim numbers in your system must have two parts) doesn't actually mean anything until you've actually defined how arithmetic works using your new number system. Both EFQ and I have pointed out that you get undesirable results (by which I mean results which lead to inconsistency) when you attempt arithmetic on your numbers (using the definition of + and • which *you* supplied). Until you show how arithmetic works in your system and that arithmetic is actually consistent in your system, you can't claim anything about the difference between two intervals in your system. > If there is zero difference between the above to intervals then they > are identical, since they are not identical then there is a non zero > difference. Having no difference in length and having no difference at all are not the same thing. (As an analogy, the set of even numbers and the set of natural numbers are both exactly the same size, but that doesn't mean they are exactly the same set.) André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 00:55 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! |
| Message-ID | <lIidnes9MphbHeHAnZ2dnUU7-VudnZ2d@giganews.com> |
| In reply to | #457956 |
On 9/14/2019 12:53 AM, peteolcott wrote: > On 9/13/2019 8:30 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). >> >> The line segment [3, 4) contains exactly one point more than the segment >> (3, 4). It is not "longer". Do you know any measure theory? >> >> It may be PO-longer but (a) will you be able to say what PO-longer >> really is (without waffling), and (b) will anyone care? >> >>> There is a geometric point immediately adjacent to 3.0 on the number >>> line. >> >> Translation: there is PO-geometric PO-point immediately PO-adjacent to 3.0 >> on the PO-number line. I am sure there is. Does anyone care? >> >>> 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. >> >> After initially appearing to want to answer questions about these >> PO-infinitesimals, you seem to have given up. I spent some time on a >> reply to your first round of answers, but you seem to a abandoned that >> sub-thread. I won't make the mistake of spending time on a reply in >> future! >> > > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > YOU LIED !!! > > On 9/14/2019 12:51 AM, peteolcott wrote:> On 9/12/2019 8:00 PM, 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. > >> > > > > > > https://en.wikipedia.org/wiki/Straw_man > > Intentional deceptive straw_man WHY LIE? Does lying give you kicks? > > > > IT IS CLEAR THAT I HAVE BEEN ALWAYS USING REAL ENDPOINTS. > > > > YOUR SWITCH TO INTEGERS IS PRETTY DAMN STUPID. > > DID YOU THINK YOU WOULD GET AWAY WITH THAT? > > > > The first point in this interval: (0.0, 1.0] very obviously > > comes immediately after the first point in this interval: [0.0, 1.0]. > > > > > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 11:33 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! |
| Message-ID | <zfSdncZ1cOZJlxzAnZ2dnUU7-dPNnZ2d@giganews.com> |
| In reply to | #458228 |
On 9/17/2019 1:47 AM, Arnaud Fournet wrote: > Le lundi 16 septembre 2019 21:57:49 UTC+2, peteolcott a écrit : >> On 9/16/2019 12:57 PM, Arnaud Fournet wrote: >>> Le lundi 16 septembre 2019 16:31:26 UTC+2, peteolcott a écrit : >>>> On 9/15/2019 12:32 PM, Arnaud Fournet wrote: >>>>> Le dimanche 15 septembre 2019 04:44:49 UTC+2, peteolcott a écrit : >>>>>> On 9/14/2019 5:46 PM, Arnaud Fournet wrote: >>>>>>> Le samedi 14 septembre 2019 18:36:29 UTC+2, peteolcott a écrit : >>>>>>>> On 9/14/2019 1:15 AM, Arnaud Fournet wrote: >>>>>>>>> Le samedi 14 septembre 2019 07:55:24 UTC+2, peteolcott a écrit : >>>>>>>>>> On 9/14/2019 12:53 AM, peteolcott wrote: >>>>>>>>>>> On 9/13/2019 8:30 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). >>>>>>>>>>>> >>>>>>>>>>>> The line segment [3, 4) contains exactly one point more than the segment >>>>>>>>>>>> (3, 4). It is not "longer". Do you know any measure theory? >>>>>>>>>>>> >>>>>>>>>>>> It may be PO-longer but (a) will you be able to say what PO-longer >>>>>>>>>>>> really is (without waffling), and (b) will anyone care? >>>>>>>>>>>> >>>>>>>>>>>>> There is a geometric point immediately adjacent to 3.0 on the number >>>>>>>>>>>>> line. >>>>>>>>>>>> >>>>>>>>>>>> Translation: there is PO-geometric PO-point immediately PO-adjacent to 3.0 >>>>>>>>>>>> on the PO-number line. I am sure there is. Does anyone care? >>>>>>>>>>>> >>>>>>>>>>>>> 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. >>>>>>>>>>>> >>>>>>>>>>>> After initially appearing to want to answer questions about these >>>>>>>>>>>> PO-infinitesimals, you seem to have given up. I spent some time on a >>>>>>>>>>>> reply to your first round of answers, but you seem to a abandoned that >>>>>>>>>>>> sub-thread. I won't make the mistake of spending time on a reply in >>>>>>>>>>>> future! >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> YOU LIED !!! >>>>>>>>>>> >>>>>>>>>>> On 9/14/2019 12:51 AM, peteolcott wrote:> On 9/12/2019 8:00 PM, 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. >>>>>>>>>>> >> >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> > https://en.wikipedia.org/wiki/Straw_man >>>>>>>>>>> > Intentional deceptive straw_man WHY LIE? Does lying give you kicks? >>>>>>>>>>> > >>>>>>>>>>> > IT IS CLEAR THAT I HAVE BEEN ALWAYS USING REAL ENDPOINTS. >>>>>>>>>>> > >>>>>>>>>>> > YOUR SWITCH TO INTEGERS IS PRETTY DAMN STUPID. >>>>>>>>>>> > DID YOU THINK YOU WOULD GET AWAY WITH THAT? >>>>>>>>>>> > >>>>>>>>>>> > The first point in this interval: (0.0, 1.0] very obviously >>>>>>>>>>> > comes immediately after the first point in this interval: [0.0, 1.0]. >>>>>>>>>>> > >>>>>>>>>>> > >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> -- >>>>>>>>>> Copyright 2019 Pete Olcott All rights reserved >>>>>>>>>> >>>>>>>>>> "Great spirits have always encountered violent >>>>>>>>>> opposition from mediocre minds." Albert Einstein >>>>>>>>> >>>>>>>>> This post of yours contains nothing new, psycho-shitter. >>>>>>>>> >>>>>>>> >>>>>>>> Don't you get sick of the smell of your big farts? >>>>>>> >>>>>>> Once again talking about yourself, psycho-shitter. >>>>>>> >>>>>> >>>>>> As it turns out I am (no matter how crazy it sounds) I am the >>>>>> judge of all. I may make Christ's words perfectly literal >>>>>> thus you will be judged by your own words, big farty party. >>>>> >>>>> you're a total shithead. >>>>> Who's gonna take you in earnest, psycho-shitter? >>>>> >>>> >>>> When you meet me at the gates of the Kingdom of Heaven and you >>>> find that I am the gatekeeper things might get much more real. >>>> I could forgive your blasphemy and say welcome in, or I could say >>>> depart from me you evil doer. >>> >>> Anyway, you're not Heaven's gatekeeper, psycho-shitter. No doubt. >>> >> >> >> That woefully fallible humans have no doubt is not at all the same thing >> as logically justified complete certainty. The most horrendous human >> error (with the worst detrimental consequences) is that humans have no doubt >> and are none-the-less incorrect. > > Anyway, your sin is that you believe you can reconfigure humanity into 0/1 bits that function logically. Does not make any sense. > I am not saying this. My [ What's in it for me ] adaptation of Christ's Gospel will cause humanity to become benevolent because they will finally understand that selflessness maximizes their own peace and joy. If everyone in the world is looking out for your own best self-interests, then you don't have to. >> >> People asserting they belong to a certain religious group kill many innocent >> civilians having no doubt that this is the will of God. > > I hope that the crimes of Islamists do not prove you are God (or Allah)... > easy, dude, easy... > They are Satanists: https://en.wikipedia.org/wiki/Shaitan https://en.wikipedia.org/wiki/Iblis They claim that they are Islamists yet are unaware that they lie even to themselves. I made the laws of God much simpler making it much more difficult for people to be lead astray: Love one another with as much empathy as possible. This single law will be applied to everyone equally: Matthew 7:16 (KJV) 16 Ye shall know them by their fruits. 20 Wherefore by their fruits ye shall know them. Benevolence versus Malevolence, beneficial versus harmful. -- 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 | 2019-09-14 21:25 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <XeqdnVQWNuiBPODAnZ2dnUU7-SXNnZ2d@giganews.com> |
| In reply to | #457950 |
On 9/14/2019 8:24 PM, George Greene wrote: > On Wednesday, September 11, 2019 at 7:32:15 PM UTC-4, peteolcott wrote: >> My infinitesimal number system forms a bijection between the integers and >> all of the geometric points on a number line. > > No it doesn't. > > >> We already know there is a bijection between all of the geometric points >> on a number line and the set of real numbers. > > Right. > >> >> Therefore the set of integers and the set of reals are the same size >> and Cantor was wrong about cardinality. > > Well, if you had any such bijecion, but you don't. > Everybody else is wondering if you even know what "bijection" even means. > There is a simple diagonal argument PROVING that these points don't map > to the integers. > Yes I know that. It is not proving what it thinks it is proving. It shows that many Real numbers are not accounted for by integers. If we look at Geometric points on the number line and have the Infinitesimal number system, we can count all of them. (0.0, 1.0] has one more point at the end than (0.0, 1.0). The first interval is exactly 1.0 long and the second interval is infinitesimally shorter than the first one. -- 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 10:26 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <OZydnYvqYuUsNOLAnZ2dnUU7-efNnZ2d@giganews.com> |
| In reply to | #457950 |
On 9/15/2019 7:02 AM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/14/2019 10:19 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/14/2019 9:29 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> >>>>>> On 9/14/2019 8:22 PM, George Greene wrote: >>>>>>> On Wednesday, September 11, 2019 at 8:30:38 PM UTC-4, peteolcott wrote: >>>>>>>>>> We already know there is a bijection between all of the geometric points >>>>>>>>>> on a number line and the set of real numbers. >>>>>>> >>>>>>> True. >>>>>> >>>>>> Someone corrected my on this. >>>>>> Some of the numbers on the number line (like PI) are not Real numbers. >>>>> >>>>> What criteria do you use to tell if you should take someone's >>>>> corrections? Because whoever it was got it wrong. pi (if you mean the >>>>> pi we all know and love) is a real number (written with a lower case >>>>> "r".) >>>>> >>>>> In fact, the two correspond exactly. The real numbers are the algebraic >>>>> abstraction of the concept of a continuous unbounded line. >>>> >>>> OK great that makes things simpler. I was thinking that irrational numbers >>>> were not real. My correction has been corrected, thanks. >>> >>> Why do you believe me rather than whoever it was that told you >>> otherwise? >> >> I looked it up. > > Ah. And presumably what you found, despite being conventional wisdom, > did not cause you to think you might be wrong about anything you care > about. > >>> Any why do you believe me about this but not about other >>> things? >>> >> >> The other things are merely your conformity to common misconceptions. > > Such as pi being a real number? Did you look up what an open interval > is? The trouble is that that is a tad more complicated than pi ∈ R, so > you probably got lost after a few sentences. But if you can press on > just a little bit you can also find out whether there is a first element > in (0, 1) just be looking it up. > 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 clearly specifies that there is a point immediately after A and before B. These points don't magically disappear because there is no conventional way to directly reference them. -- 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 18:24 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <rdedndyh8t0thB3AnZ2dnUU7-YudnZ2d@giganews.com> |
| In reply to | #458436 |
On 9/16/2019 6:21 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > <cut> >> 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 clearly specifies that there is a point immediately after A and >> before B. > > No it doesn't. I don't think there is any way forward here because you > are simply reading things into that text that are not there. Normally > I'd suggest you go and read about the development of the reals, but > that's a non-starter for you. When we remove the beginning 0.5 from [0.0, 2.0] we derive [0.5, 2.0] with a first point of 0.5. When we remove the beginning 0.1 from [0.0, 2.0] we derive [0.1, 2.0] with a first point of 0.1. When we remove the beginning 0.0001 from [0.0, 2.0] we derive [0.0001, 2.0] with a first point of 0.0001. So when we remove a single point from the beginning of [0.0, 1.0] we end up with (0.0, 1.0] with beginning point that cannot be named. WE DON'T END UP WITHOUT A BEGINNING POINT. > > Another thing I'd suggest (to an actual student wanting to learn) would > be to consider why (0, 1) is called an /open/ interval. When you learn > what an open set is, you'll learn why you are wrong. > > What's actually going on is that you are thinking about a number line > that does not have the right properties. This is the classic crank > problem: your number line and your intervals are not ours, but if you > were to say that the PO-interval (0, 1] has a first point, no one would > care. > >> These points don't magically disappear because there is no conventional way >> to directly reference them. > > There are, and always have been, conventional ways to directly reference > these non-existent numbers. It's because even you have been able to > reference them that I, and others, have been able to tell you they don't > exist. Here are just a few of the ways of referring to one such > non-extent number: > > the number immediately adjacent to 0 in [0, 1] > the first number in (0, 1] > min (0, 1] > x ∈ (0, 1] s.t. ∀y ∈ (0, 1] x <= y > > Neither naming nor defining things make them exist. > -- 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 22:43 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <j66dncFr9pPeyx3AnZ2dnUU7-XvNnZ2d@giganews.com> |
| In reply to | #458492 |
On 9/16/2019 9:34 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/16/2019 8:10 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/16/2019 6:21 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> <cut> >>>>>> 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 clearly specifies that there is a point immediately after A and >>>>>> before B. >>>>> >>>>> No it doesn't. I don't think there is any way forward here because you >>>>> are simply reading things into that text that are not there. Normally >>>>> I'd suggest you go and read about the development of the reals, but >>>>> that's a non-starter for you. >>>> >>>> When we remove the beginning 0.5 from [0.0, 2.0] we derive [0.5, 2.0] >>>> with a first point of 0.5. >>> >>> You could be clearer, but you are not wrong: >>> >>> [0, 2] \ [0, 0.5) = [0.5, 2] with first point 0.5 >>> >>> but >>> >>> [0, 2] \ [0, 0.5] = (0.5, 2] with no first point. >> >> You keep getting confused by this. >> [0, 2] and we remove the very first point (0, 2] >> then necessarily all of the rest of the points remain. > > This is true. I did not say otherwise. > >> Just because we don't have a real number to express the >> first point does not prove that there is no first point >> as everyone assumes. > > No one assumes it. It's proven. If you look at it on the basis of real numbers it is proven. If you look at it on the basis of infinitesimal numbers it is not proven. > >> all of the rest of the points remain and they remain in >> their same order. > > They do indeed. I don't see what you think I am confused by. You are > simply assuming the set of remaining points has a least member in that > "same order". It does not, for the reasons that have been pointed out > many times. > > The following is important, but you don't read what people write, do > you? > >>> Note that I am talking about real intervals because that is the context >>> of the definition you cite above. PO-points and PO-intervals are not >>> interesting to me. Can you at least agree that for the real interval >>> (0, 1] there is no first number? > > I very much hope (against experience) that you will answer this question. > >>> Despite prior experience, you might possibly answer this question >>> because you seem to accept that, for reals at east, if x = min (0, 1] >>> then x/2 must be be in the real interval (0, 1] and yet less than min >>> (0, 1]. I say you accept this, because I've seen you claim that your >>> "points" are not subject to this argument. > > If your points are no real numbers, then can only keep talking about > reals and real intervals until you defined PO-points and PO-intervals. > -- 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 | 2019-09-16 23:12 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlpq0g$r2t$1@dont-email.me> |
| In reply to | #458510 |
On 2019-09-16 9:43 p.m., peteolcott wrote: > On 9/16/2019 9:34 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> Just because we don't have a real number to express the >>> first point does not prove that there is no first point >>> as everyone assumes. >> >> No one assumes it. It's proven. > > If you look at it on the basis of real numbers it is proven. > If you look at it on the basis of infinitesimal numbers it is not proven. We can't prove anything on the basis of infinitesimals until you actually explain how infinitesimals work. That means not just coming up with your notation R[I] where R is the real part and I the infinitesimal part, but also explaining how arithmetic works over these and how to evaluate relations like <, > etc. I've already pointed out that the definition of multiplication you offered doesn't work, but you've never come back to that point and offered a coherent account of how your system works. So here's a simple question: What is the actual *point* of having the infinitesimal portion in your numbers? You claim that your infinitesimal is indivisible such that there does not exist x such that 0.0[0] < x < 0.0[1]. But, for the real numbers, for all y and z such that y < z there is *always* some x such that y < z < z. So if the 'real' portion of your R[I] is actually real, we should be able to have some number a[0] which is less than 0.0[1]. Given this, any number expressible as R[I] should also be expressible as a simple real without making use of the infinitesimal portion. What makes your system any more useful than the following 'system': In my intermediatesimal system, every number consists of a rational part Q, and hundredths portion [H] which specifies an offsets in hundredths. So, for example, ⅜[5] specifies the rational number ⅝ with an offset of 5 one hundredths. Of what use would such a system be given that any number expressible in this system could be expressible by the rational portion alone? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 22:19 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <q_Gdne4MsYTKPxzAnZ2dnUU7-fPNnZ2d@giganews.com> |
| In reply to | #458510 |
On 9/17/2019 9:55 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 9:34 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/16/2019 8:10 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>
>>>>>>>> On 9/16/2019 6:21 PM, Ben Bacarisse wrote:
>>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>> <cut>
>>>>>>>>>> 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 clearly specifies that there is a point immediately after A and
>>>>>>>>>> before B.
>>>>>>>>>
>>>>>>>>> No it doesn't. I don't think there is any way forward here because you
>>>>>>>>> are simply reading things into that text that are not there. Normally
>>>>>>>>> I'd suggest you go and read about the development of the reals, but
>>>>>>>>> that's a non-starter for you.
>>>>>>>>
>>>>>>>> When we remove the beginning 0.5 from [0.0, 2.0] we derive [0.5, 2.0]
>>>>>>>> with a first point of 0.5.
>>>>>>>
>>>>>>> You could be clearer, but you are not wrong:
>>>>>>>
>>>>>>> [0, 2] \ [0, 0.5) = [0.5, 2] with first point 0.5
>>>>>>>
>>>>>>> but
>>>>>>>
>>>>>>> [0, 2] \ [0, 0.5] = (0.5, 2] with no first point.
>>>>>>
>>>>>> You keep getting confused by this.
>>>>>> [0, 2] and we remove the very first point (0, 2]
>>>>>> then necessarily all of the rest of the points remain.
>>>>>
>>>>> This is true. I did not say otherwise.
>>>>>
>>>>>> Just because we don't have a real number to express the
>>>>>> first point does not prove that there is no first point
>>>>>> as everyone assumes.
>>>>>
>>>>> No one assumes it. It's proven.
>>>>
>>>> If you look at it on the basis of real numbers it is proven.
>>>
>>> I am glad you accept that. It is proven for any set that like those in
>>> the article you cited so you will forgive me (an others) for think you
>>> were talking about such sets.
>>>
>>>> If you look at it on the basis of infinitesimal numbers it is not
>>>> proven.
>>>
>>> It is also proven for all infinitesimals defined by actual
>>> mathematicians, but you can be forgiven for not know this because of the
>>> value you place on ignorance.
>>>
>>> It will also be true of your infinitesimals unless they are useless.
>>> You claim they are countable so they do not serve as a model for points
>>> on a line, but ayway, you can't define them (and trying to get you to
>>> will be like getting blood out of a stone) so exactly why they are
>>> useless will remain a mystery.
>>
>> Keith Thompson understands that they could refute differing sized
>> cardinality of infinite sets.
>
> No he doesn't. The trouble is, you don't understand what he's saying.
> In fact he agrees with me though he puts it more cautiously. I'll leave
> it here for those that /can/ follow:
>
I SUMMED IT UP MORE CONCISELY HERE:
THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-17 21:23 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qls7vu$1l9$1@dont-email.me> |
| In reply to | #458635 |
On 2019-09-17 9:19 p.m., peteolcott wrote:
> On 9/17/2019 9:55 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
<snip>
>>> Keith Thompson understands that they could refute differing sized
>>> cardinality of infinite sets.
>>
>> No he doesn't. The trouble is, you don't understand what he's saying.
>> In fact he agrees with me though he puts it more cautiously. I'll leave
>> it here for those that /can/ follow:
>>
>
> I SUMMED IT UP MORE CONCISELY HERE:
>
> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
> 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
I'd asked earlier but got no response, so I'll ask again.
Do you accept that there is no *greatest* integer?
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-17 22:31 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <UP6dnfNIrbNsORzAnZ2dnUU7-XfNnZ2d@giganews.com> |
| In reply to | #458637 |
On 9/17/2019 10:23 PM, André G. Isaak wrote:
> On 2019-09-17 9:19 p.m., peteolcott wrote:
>> On 9/17/2019 9:55 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>
> <snip>
>
>>>> Keith Thompson understands that they could refute differing sized
>>>> cardinality of infinite sets.
>>>
>>> No he doesn't. The trouble is, you don't understand what he's saying.
>>> In fact he agrees with me though he puts it more cautiously. I'll leave
>>> it here for those that /can/ follow:
>>>
>>
>> I SUMMED IT UP MORE CONCISELY HERE:
>>
>> THERE IS A POINT ON THE NUMBER LINE IMMEDIATELY ADJACENT TO 0
>> 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
>
> I'd asked earlier but got no response, so I'll ask again.
>
> Do you accept that there is no *greatest* integer?
>
> André
>
Infinity is a process rather than a value, thus there is no greatest
integer and all infinite sets are likewise this exact same limitlessness.
Integer N = 0;
HERE:
N = N + 1;
goto HERE;
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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