Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
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 |
Back to article view | Back to sci.math
This discussion starts older than the indexed window; earlier articles aren't shown. The article labeled Started by
below is the oldest one visible, not the original post.
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
Page 5 of 9 — ← Prev page 1 2 3 4 [5] 6 7 8 9 Next page →
| 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 | #458695 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #458698 |
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 */
[toc] | [prev] | [next] | [standalone]
| 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 | #458751 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #458695 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #457956 |
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.
[toc] | [prev] | [next] | [standalone]
| 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 | #458024 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #458033 |
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.
[toc] | [prev] | [next] | [standalone]
| 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 | #458035 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #458100 |
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.
[toc] | [prev] | [next] | [standalone]
| 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 | #458104 |
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
[toc] | [prev] | [next] | [standalone]
| 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 | #458150 |
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.
[toc] | [prev] | [next] | [standalone]
| 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 | #458151 |
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.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-13 11:40 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <HMSdnT5AD-H0W-bAnZ2dnUU7-XvNnZ2d@giganews.com> |
| In reply to | #458152 |
On 9/13/2019 10:56 AM, André G. Isaak wrote: > 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 + b[x + y] > a[x] • b[y] = ? a * b[x * y] > > André > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-13 11:03 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlgi61$v3a$1@dont-email.me> |
| In reply to | #458155 |
On 2019-09-13 10:40 a.m., peteolcott wrote: > On 9/13/2019 10:56 AM, André G. Isaak wrote: >> 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 + b[x + y] > >> a[x] • b[y] = ? > a * b[x * y] Now have you ever actually tried applying this to real problems to verify that it works? 0[3] + 0[3] = 0[6] OK. That seems sort of reasonable. 0[3] • 0[3] = 0[9] But do you really want to claim that multiplying two numbers which are just *slightly* larger than zero is going to give you a result which is *greater* than the sum of those two numbers? Compare that with actual math: 0.1 + 0.1 = 0.2 0.1 • 0.1 = 0.01 André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-13 12:48 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <TaednY3zgK_vS-bAnZ2dnUU7-QudnZ2d@giganews.com> |
| In reply to | #458160 |
On 9/13/2019 12:03 PM, André G. Isaak wrote: > On 2019-09-13 10:40 a.m., peteolcott wrote: >> On 9/13/2019 10:56 AM, André G. Isaak wrote: >>> 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 + b[x + y] >> >>> a[x] • b[y] = ? >> a * b[x * y] > > > Now have you ever actually tried applying this to real problems to verify that it works? > > 0[3] + 0[3] = 0[6] > > OK. That seems sort of reasonable. > > 0[3] • 0[3] = 0[9] > > But do you really want to claim that multiplying two numbers which are just *slightly* larger than zero is going to give you a result which is *greater* than the sum of those two numbers? > > Compare that with actual math: > > 0.1 + 0.1 = 0.2 > 0.1 • 0.1 = 0.01 > > André > All of this is beside the point. The whole point was to simply prove that Cantor was wrong by making the set of all numbers countable with the set of integers. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-13 12:25 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlgmvm$s6g$1@dont-email.me> |
| In reply to | #458163 |
On 2019-09-13 11:48 a.m., peteolcott wrote: > On 9/13/2019 12:03 PM, André G. Isaak wrote: >> On 2019-09-13 10:40 a.m., peteolcott wrote: >>> On 9/13/2019 10:56 AM, André G. Isaak wrote: >>>> 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 + b[x + y] >>> >>>> a[x] • b[y] = ? >>> a * b[x * y] >> >> >> Now have you ever actually tried applying this to real problems to >> verify that it works? >> >> 0[3] + 0[3] = 0[6] >> >> OK. That seems sort of reasonable. >> >> 0[3] • 0[3] = 0[9] >> >> But do you really want to claim that multiplying two numbers which are >> just *slightly* larger than zero is going to give you a result which >> is *greater* than the sum of those two numbers? >> >> Compare that with actual math: >> >> 0.1 + 0.1 = 0.2 >> 0.1 • 0.1 = 0.01 >> >> André >> > > All of this is beside the point. The whole point was to simply > prove that Cantor was wrong by making the set of all numbers > countable with the set of integers. If your new number system doesn't even work consistently for basic arithmetic, then how can you claim to have refuted anything with it? This is the thing you consistently don't get: Accepted formal systems are comprised of interconnected pieces which have been shown to work together to form a consistent and coherent system. Anytime you add to, or subtract from, or change anything in an existing system there is a very good chance that *every* *single* *thing* within that system will break. Determining which things will and won't work in a new system requires that you actually sit down and rigorously define every single thing within that system to verify that all of your definitions work together consistently and actually do what you claim they do. You, however, always skip this step because it is 'tedious detail' and assume that a bunch of different definitions drawn from a bunch of separate sources are somehow going to automatically cohere with one another and with your new additions. 99.999% of the time they will not and all will need to be revised. Once you have a set of definitions that you are satisfied with, the next step is to do absolutely everything in your power to try to make your system *break*. That's the only way to find problems which need to be resolved. Again, you don't do this, so others here attempt to help you with this at which point you accuse them of being in perpetual 'rebuttal' mode. Really, though it is *you* that needs to get into the habit of being in perpetual rebuttal mode. And the thing that you absolutely *can't* do is simply dismiss it when someone points out a problem for you like you do above. Having arithmetic actually work is not "beside the point" when dealing with a theory of the number line. So at this point I'd strongly recommend that you just stop making additions to this new 'theory' and instead sit down and read up on the last 400 years or so of mathematics and see what people have already been able to achieve with infinitesimals and what things people have failed to achieve with infinitesimals. Then maybe you can return to your problem without making such obvious mistakes. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-13 22:35 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlhqmj$81b$1@dont-email.me> |
| In reply to | #458163 |
On 2019-09-13 11:48 a.m., peteolcott wrote: > On 9/13/2019 12:03 PM, André G. Isaak wrote: >> On 2019-09-13 10:40 a.m., peteolcott wrote: >>> On 9/13/2019 10:56 AM, André G. Isaak wrote: >>>> On 2019-09-13 9:13 a.m., André G. Isaak wrote: >>>>> On 2019-09-13 9:01 a.m., peteolcott wrote: >>>>>> 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. <snip> > All of this is beside the point. The whole point was to simply > prove that Cantor was wrong by making the set of all numbers > countable with the set of integers. Just to add one further point to my earlier, more detailed, response, even if the alleged bijection which you are unwilling to state actually exists, since you acknowledge above that you are *not* talking about the reals, this would not show that Cantor was wrong because Cantor *was* talking about the reals. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 16:42 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <n5GdnSMrN6Mtw-DAnZ2dnUU7-cfNnZ2d@giganews.com> |
| In reply to | #458221 |
On 9/13/2019 11:35 PM, André G. Isaak wrote: > On 2019-09-13 11:48 a.m., peteolcott wrote: >> On 9/13/2019 12:03 PM, André G. Isaak wrote: >>> On 2019-09-13 10:40 a.m., peteolcott wrote: >>>> On 9/13/2019 10:56 AM, André G. Isaak wrote: >>>>> On 2019-09-13 9:13 a.m., André G. Isaak wrote: >>>>>> On 2019-09-13 9:01 a.m., peteolcott wrote: > >>>>>>> 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. > > <snip> > >> All of this is beside the point. The whole point was to simply >> prove that Cantor was wrong by making the set of all numbers >> countable with the set of integers. > > Just to add one further point to my earlier, more detailed, response, even if the alleged bijection which you are unwilling to state actually exists, since you acknowledge above that you are *not* talking about the reals, this would not show that Cantor > was wrong because Cantor *was* talking about the reals. > > André > Cantor showed that the cardinality of reals is larger than the cardinality of integers. The cardinality of all numbers is at least as large as the cardinality of reals because all numbers includes reals as a subset. If every element of all numbers is countable then the cardinality of integers is the same as the cardinality of all numbers. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-13 11:28 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <rNCdndfYWNtfXubAnZ2dnUU7-TPNnZ2d@giganews.com> |
| In reply to | #458151 |
On 9/13/2019 10:13 AM, 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." Yes you are correct I was wrong about this. The next number may not be a real number. I had assumed that it was. Now that we find that it lacks at least one of the properties of real numbers it must be some other kind of number besides a real number. > > >> 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 > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 18:00 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- COMPLETE (Andy Goofed) |
| Message-ID | <e8qdnTvIS6aD7ODAnZ2dnUU7-S_NnZ2d@giganews.com> |
| In reply to | #458150 |
On 9/14/2019 5:44 PM, Andy Walker wrote:
> On 14/09/2019 17:34, peteolcott wrote:
> [...]
>> My ONLY point is that Cantor was wrong
>
> Not so. As others have pointed out, you seem to think so
> because you have a rather eccentric [to say the least] view of what
> a number is, and have a closed mind to alternative views. One of
> the things that [esp] research mathematicians learn is that there
> are often many different perfectly correct views of how things work.
> Plus many incorrect views.
>
>> 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}:
>> Integer N = 0;
>> HERE:
>> N = N + 1;
>> goto HERE;
>
> That depends on how you define "infinity". It is not a
> "real" number, but there are alternative views of numbers in which
> there are accessible infinities. Eg, the [childish] playground
> game "My dad has more than your dad" can be modelled by each player
> in turn calling out a number, and the largest number wins; there
> is an obvious win to win if you play last, and the "value" of being
> the last player is "infinite" in that you can beat any finite call.
> In that sense, "infinity" merely means "sufficiently large". May
> also be worth noting that standard map projections can turn finite
> points into infinities and vice versa; cf the "line at infinity"
> in projective geometry, and the "horizon" in perspective drawing.
>
>> 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.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
Page 5 of 9 — ← Prev page 1 2 3 4 [5] 6 7 8 9 Next page →
Back to top | Article view | sci.math
csiph-web