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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 | 2019-09-11 12:05 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) |
| Message-ID | <er6dnc11p8XwtOTAnZ2dnUU7-d9QAAAA@giganews.com> |
On 9/11/2019 2:31 AM, Reinhardt Behm wrote: > On 9/10/19 11:38 PM, peteolcott wrote: >> The next real number after 3.0 is the geometric point on the number >> line that is immediately adjacent to 3.0 on its right side. This geometric >> point is an infinitesimally larger than 3.0: encoded as the first point in >> the interval: (3,4] > > And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. > I specified a whole Infinitesimal number system: Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number of geometric points offset from the real part. 0.0[1,∞] specifies the entire set of geometric points with a value greater than zero on the number line which self-evidently corresponds to the entire set of positive reals. Notice that this entire set is countable using the set of positive integers. Copyright 2019 Pete Olcott -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 18:32 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <sqydnZDTcotlHuTAnZ2dnUU7-bXNnZ2d@giganews.com> |
| In reply to | #457916 |
On 9/11/2019 12:37 PM, Fred wrote: > On 11/09/2019 18:05, peteolcott wrote: >> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>> On 9/10/19 11:38 PM, peteolcott wrote: >>>> The next real number after 3.0 is the geometric point on the number >>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>> the interval: (3,4] >>> >>> And between 3.0 and your "next" number (xnext) to the right is another real number: (3.0+xnext) / 2. >>> >> >> I specified a whole Infinitesimal number system: >> Real_Part[Infinitesimal_Part] where the Infinitesimal_Part is the number >> of geometric points offset from the real part. >> >> 0.0[1,∞] specifies the entire set of geometric points with a value >> greater than zero on the number line which self-evidently corresponds >> to the entire set of positive reals. >> >> Notice that this entire set is countable using the set of positive integers. > > If your "infinitesimal number system" contains the usual real numbers and some other things as well, it cannot have a smaller cardinality than just the usual real numbers on their own. > > My infinitesimal number system forms a bijection between the integers and all of the geometric points on a number line. We already know there is a bijection between all of the geometric points on a number line and the set of real numbers. Therefore the set of integers and the set of reals are the same size and Cantor was wrong about cardinality. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 20:03 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <18OdnXrmgfvKBOTAnZ2dnUU7-efNnZ2d@giganews.com> |
| In reply to | #457950 |
On 9/11/2019 7:42 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > <cut> >>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>>>> On 9/10/19 11:38 PM, peteolcott wrote: >>>>>> The next real number after 3.0 is the geometric point on the number >>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>>>> the interval: (3,4] > > There is no next real number after 3.0. There is not even a next rational > number after 3.0, and the rationals /are/ countable! I.e. you don't > need there to be a successor function on points that respects the > usual ordering of points to get a countable set between 3 and 4. As it > is, you open yourself up to the obvious problem: The line segment [3.0, 4.0) is exactly one geometric point longer than (3.0. 4.0). There is a geometric point immediately adjacent to 3.0 on the number line. This geometric point does correspond to a number because it is on the number line. Now I have to correct my prior reasoning. All of the geometric points on the number line correspond to all of the numbers that exist. Some of these are not real numbers. Since we can count all of these numbers with integers using the infinitesimal number system we have proven that the set of real numbers is not larger than the set of integers. Real_Part[Infinitesimal_Offset] 0.0[1 to ∞] forms a bijection between the positive integers and all of the positive numbers through all of the positive points on the number line. Copyright 2019 Pete Olcott > >>>>> And between 3.0 and your "next" number (xnext) to the right is >>>>> another real number: (3.0+xnext) / 2. > <cut> >> My infinitesimal number system forms a bijection between the integers and >> all of the geometric points on a number line. > > Ignoring questions won't make you right (but it will allow yo to keep > boasting). > > Talking of boasting, it's now nine months since you first claimed to > have an impossible "actual Turing machine" "fully encoded". No sign of > you ever posting it of course. > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 20:59 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <FtOdnVZus7sOO-TAnZ2dnUU7-e_NnZ2d@giganews.com> |
| In reply to | #457956 |
On 9/11/2019 8:50 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/11/2019 7:42 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>>>>>> On 9/10/19 11:38 PM, peteolcott wrote: >>>>>>>> The next real number after 3.0 is the geometric point on the number >>>>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>>>>>> the interval: (3,4] >>> >>> There is no next real number after 3.0. There is not even a next rational >>> number after 3.0, and the rationals /are/ countable! I.e. you don't >>> need there to be a successor function on points that respects the >>> usual ordering of points to get a countable set between 3 and 4. As it >>> is, you open yourself up to the obvious problem: >> >> The line segment [3.0, 4.0) is exactly one geometric point longer than >> (3.0. 4.0). > > I was going to say "correct!" because |[3, 4) \ (3, 4)| is indeed 1, but > that was before I saw that not all your PO-geometric points are real > numbers. Since I don't know what PO-geometric points really are I'll > just take your word for it. > >> There is a geometric point immediately adjacent to 3.0 on the number line. >> This geometric point does correspond to a number because it is on the >> number line. >> >> Now I have to correct my prior reasoning. All of the geometric points on >> the number line correspond to all of the numbers that exist. Some of these >> are not real numbers. >> >> Since we can count all of these numbers with integers using the infinitesimal >> number system > > You can not count all of these numbers with integers. You can not count > all of the reals let alone the PO-geometric points that (according to > you) includes things that are not real numbers. > >> we have proven that the set of real numbers is not larger >> than the set of integers. > > Saying "we can count..." is not a proof of counting. > >> Real_Part[Infinitesimal_Offset] >> >> 0.0[1 to ∞] forms a bijection between the positive integers and all of >> the positive numbers through all of the positive points on the number >> line. > > You can't mean that. Well, actually I know you might mean that, but > it's obviously wrong. I'll say why, but only if you agree to answer > questions about your claims in good faith -- you have to be prepared to > learn why you are wrong otherwise it's just a waste of both of our time. > (1) Do you understand that all of the points on a number line are all of the numbers? (2) Do you understand that a bijection between the integers and these points would make these points countable? -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 22:16 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <K_OdnfvuReoCJeTAnZ2dnUU7-YOdnZ2d@giganews.com> |
| In reply to | #457964 |
On 9/11/2019 10:07 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/11/2019 8:50 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/11/2019 7:42 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> <cut> >>>>>>>> On 9/11/2019 2:31 AM, Reinhardt Behm wrote: >>>>>>>>> On 9/10/19 11:38 PM, peteolcott wrote: >>>>>>>>>> The next real number after 3.0 is the geometric point on the number >>>>>>>>>> line that is immediately adjacent to 3.0 on its right side. This geometric >>>>>>>>>> point is an infinitesimally larger than 3.0: encoded as the first point in >>>>>>>>>> the interval: (3,4] >>>>> >>>>> There is no next real number after 3.0. There is not even a next rational >>>>> number after 3.0, and the rationals /are/ countable! I.e. you don't >>>>> need there to be a successor function on points that respects the >>>>> usual ordering of points to get a countable set between 3 and 4. As it >>>>> is, you open yourself up to the obvious problem: >>>> >>>> The line segment [3.0, 4.0) is exactly one geometric point longer than >>>> (3.0. 4.0). >>> >>> I was going to say "correct!" because |[3, 4) \ (3, 4)| is indeed 1, but >>> that was before I saw that not all your PO-geometric points are real >>> numbers. Since I don't know what PO-geometric points really are I'll >>> just take your word for it. >>> >>>> There is a geometric point immediately adjacent to 3.0 on the number line. >>>> This geometric point does correspond to a number because it is on the >>>> number line. >>>> >>>> Now I have to correct my prior reasoning. All of the geometric points on >>>> the number line correspond to all of the numbers that exist. Some of these >>>> are not real numbers. >>>> >>>> Since we can count all of these numbers with integers using the infinitesimal >>>> number system >>> >>> You can not count all of these numbers with integers. You can not count >>> all of the reals let alone the PO-geometric points that (according to >>> you) includes things that are not real numbers. >>> >>>> we have proven that the set of real numbers is not larger >>>> than the set of integers. >>> >>> Saying "we can count..." is not a proof of counting. >>> >>>> Real_Part[Infinitesimal_Offset] >>>> >>>> 0.0[1 to ∞] forms a bijection between the positive integers and all of >>>> the positive numbers through all of the positive points on the number >>>> line. >>> >>> You can't mean that. Well, actually I know you might mean that, but >>> it's obviously wrong. I'll say why, but only if you agree to answer >>> questions about your claims in good faith -- you have to be prepared to >>> learn why you are wrong otherwise it's just a waste of both of our time. >> >> (1) Do you understand that all of the points on a number line are all >> of the numbers? >> >> (2) Do you understand that a bijection between the integers and these >> points would make these points countable? > > I take it you don't want to learn why you are wrong. OK. > You could explain how the following are incorrect, the problem with that is that they are not incorrect and YOU KNOW IT SO YOU DODGE !!! (1) Do you understand that all of the points on a number line are all of the numbers? (2) Do you understand that a bijection between the integers and these points would make these points countable? -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-12 11:14 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <NeudnY8TtYJx8-fAnZ2dnUU7-X3NnZ2d@giganews.com> |
| In reply to | #457972 |
On 9/12/2019 10:33 AM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: >>>>> peteolcott <Here@Home> writes: >>>>>>> peteolcott <Here@Home> writes: > <cut> >>>>>>>> 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. > <cut> >>>>>>>> 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. > <cut> >>>>>> (1) Do you understand that all of the points on a number line are all >>>>>> of the numbers? >>>>>> >>>>>> (2) Do you understand that a bijection between the integers and these >>>>>> points would make these points countable? > <cut> >> I will answer any good faith questions in good faith. > > Oh, good. Here are a few questions to clarify what you mean. > > Q1. Did you mean to exclude a zero infinitesimal offset? > No. > Q1a: If you did mean to exclude r[0], do you write the point at, say, > exactly 1 as 1.0 with no [...] part? > > Q1b: Again, if so, would you mind writing that as 1[0] to give all > points the same form? 1[0] is the same as 1. > > Q2. What numbers can go in the "Real_Part"? All the examples you have > given use a "whole number". Can it be any real as the name > implies? Any identifiable number can go into the "real" part. π[1] is one geometric point to the right of π. > > Q3. Given two arbitrary points r1[i1] and r2[i2], is r1[i1] = r2[i2] if > and only if r1 = r2 and i1 = i2? > I think so. I can't see any exception right now. [3.0,4.0) is the same length as (3.0,4.0] as infinitesimal numbers 3.0 to 4.0[-1] is the same length as 3.0[+1] to 4.0 > Q4. You say > > "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" > > What n makes 0.0[n] equal to the point I would call 1? There is no bijection there. > > Q5. If all the points on the number line can written in the form 0.0[n] > for some n, what is the point of having your "Real_Part"? To identify it as an infinitesimal number of the infinitesimal number system. To specifically label the base part of the base/offset because there is no bijection between reals and infinitesimals having an offset. > > Q6. If, say, 0.0[23] and 0.0[24] are both points on the number line, > how do you represent the point half way between them? As you already know this is defined as non existent. There is no one half of infinitesimal. > > Q7. One can compare and do arithmetic with real numbers. Are any of > the usual relations and/or operations defined for yours? If so, > how are these defined: > > Q7a. r1[i1] < r2[i2] ? > Q7b. r1[i1] + r2[i2] ? > Q7c. r1[i1] - r2[i2] ? > Q7d. r1[i1] * r2[i2] ? > Q7e. r1[i1] / r2[i2] ? > > (I covered r1[i1] = r2[i2] in Q3.) I laid this all out previously. There is no bijection between reals and infinitesimals having an offset. Single infinitesimal quantities are indivisible. Relations and operations between infinitesimals generally operate on their base part and offset part separately. Likewise with mixed type relations and operations. > >> It really seems to me that your good faith answer to my >> above questions would necessarily prove that I am correct. > > But your (1) and (2) combine to make a hypothetical. The answers can't > prove anything, so my answering them would be as pointless and your > asking them. Sure, if there /were/ a bijection between all the points > and the integers, they (all the points) would be countable. However, > either your points are not all the points, or there is not a bijection > between your points and the integers. > It seems that I did specify a notational system that does form a bijection between integers and the set of points on a number line. The common notational convention used for intervals make it clear that the key notion of my system: [immediately adjacent points on a number line] do exist, and can be uniquely identified. -- 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 | 2019-09-12 21:00 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben |
| Message-ID | <uNSdnfHgad28ZefAnZ2dnUU7-Q3NnZ2d@giganews.com> |
| In reply to | #458037 |
On 9/12/2019 8:00 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/12/2019 10:33 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>> peteolcott <Here@Home> writes:
>>> <cut>
>>>>>>>>>> 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.
>>> <cut>
>>>>>>>>>> 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.
>>> <cut>
>>>>>>>> (1) Do you understand that all of the points on a number line are all
>>>>>>>> of the numbers?
>>>>>>>>
>>>>>>>> (2) Do you understand that a bijection between the integers and these
>>>>>>>> points would make these points countable?
>>> <cut>
>>>> I will answer any good faith questions in good faith.
>>>
>>> Oh, good. Here are a few questions to clarify what you mean.
>>>
>>> Q1. Did you mean to exclude a zero infinitesimal offset?
>>>
>> No.
>>
>>> Q1a: If you did mean to exclude r[0], do you write the point at, say,
>>> exactly 1 as 1.0 with no [...] part?
>>>
>>> Q1b: Again, if so, would you mind writing that as 1[0] to give all
>>> points the same form?
>>
>> 1[0] is the same as 1.
>>>
>>> Q2. What numbers can go in the "Real_Part"? All the examples you have
>>> given use a "whole number". Can it be any real as the name
>>> implies?
>>
>> Any identifiable number can go into the "real" part.
>
> That's unfortunately unclear. What you mean by "identifiable number"
> needs to be clarified. I have a guess, but that's no way to proceed.
>
> My guess: lbh zrna nal ahzore gung pna or jevggra qbja va fbzr svavgr
> sbez yvxr "7.1" naq "fdeg(2)". Vs fb, gur frg bs CB-trbzrgevp cbvagf vf
> vaqrrq pbhagnoyr.
>
>> π[1] is one geometric point to the right of π.
>
>>> Q3. Given two arbitrary points r1[i1] and r2[i2], is r1[i1] = r2[i2] if
>>> and only if r1 = r2 and i1 = i2?
>>>
>> I think so. I can't see any exception right now.
>
>>> Q4. You say
>>>
>>> "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"
>>>
>>> What n makes 0.0[n] equal to the point I would call 1?
>> There is no bijection there.
>
> Hm... that is not a use of words that makes sense. But Q4 is answered
> by your answer to Q3: there is no n that makes 0[n] equal to 1[0]. Can
> you confirm this?
>
> The text I quote in Q4 speaks of a bijection but in terms that are
> non-standard. (It's the "through" in "a bijection between X and Y
> though Z" that is odd.) Can you state, clearly, what sets are in
> bijection? Both "the positive numbers" and "the positive points on the
> number line" are ambiguous terms. The only clear set is first: { 0[n] |
> n ∈ Z+ }.
>
>>> Q5. If all the points on the number line can written in the form 0.0[n]
>>> for some n, what is the point of having your "Real_Part"?
>> To identify it as an infinitesimal number of the infinitesimal number system.
>
> This seems like an odd reply because your answer to Q3 says that one
> can't write 1[0] as some offset from 0, so you should be rejecting the
> premise of my question. And, because there is no n for which 0[n] =
> 1[0], different "Real_Part"s are essential simply to be able to write
> all the points.
>
>> To specifically label the base part of the base/offset because there is
>> no bijection between reals and infinitesimals having an offset.
>
> Again, can you state clearly what two sets do /not/ biject? One is
> clear: it's just R, yes?, but what "infinitesimals having an offset" are
> is not, in part because Q2 is not yet answered.
>
>>> Q6. If, say, 0.0[23] and 0.0[24] are both points on the number line,
>>> how do you represent the point half way between them?
>> As you already know this is defined as non existent.
>> There is no one half of infinitesimal.
>
> I thought you were questioning Cantor's results about the continuum?
> The continuum has the property that between every two points, there are
> infinitely many more points. If your points are a subset of the
> continuum, they may very well be countable, but no one will care about
> them.
>
>>> Q7. One can compare and do arithmetic with real numbers. Are any of
>>> the usual relations and/or operations defined for yours? If so,
>>> how are these defined:
>>>
>>> Q7a. r1[i1] < r2[i2] ?
>>> Q7b. r1[i1] + r2[i2] ?
>>> Q7c. r1[i1] - r2[i2] ?
>>> Q7d. r1[i1] * r2[i2] ?
>>> Q7e. r1[i1] / r2[i2] ?
>>>
>>> (I covered r1[i1] = r2[i2] in Q3.)
>>
>> I laid this all out previously.
>
> Where did you define r1[i1] < r2[i2]? I did not see it. In fact I did
> not see the definitions of any of these. Just cut and paste the
> definitions so they are all on one place.
>
>> There is no bijection between reals and infinitesimals having an
>> offset. Single infinitesimal quantities are indivisible.
>>
>> Relations and operations between infinitesimals
>> generally operate on their base part and offset part separately.
>
> Can you give the definitions, please?
>
>> Likewise with mixed type relations and operations.
>
> What are mixed type relations and operations? The obvious meaning
> (operations between your point and other numbers) makes no sense because
> of the "likewise".
>
>>>> It really seems to me that your good faith answer to my
>>>> above questions would necessarily prove that I am correct.
>>>
>>> But your (1) and (2) combine to make a hypothetical. The answers can't
>>> prove anything, so my answering them would be as pointless and your
>>> asking them. Sure, if there /were/ a bijection between all the points
>>> and the integers, they (all the points) would be countable. However,
>>> either your points are not all the points, or there is not a bijection
>>> between your points and the integers.
>>
>> It seems that I did specify a notational system that does form a
>> bijection between integers and the set of points on a number line.
>
> Answering my follow-up questions will clarify what sets do and do not
> biject.
>
>> The common notational convention used for intervals make it clear
>> that the key notion of my system: [immediately adjacent points on
>> a number line] do exist, and can be uniquely identified.
>
> 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 | 2019-09-13 11:48 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben |
| Message-ID | <o96dnXexb6XwVebAnZ2dnUU7-VXNnZ2d@giganews.com> |
| In reply to | #458085 |
On 9/13/2019 10:38 AM, Fred wrote:
> On 13/09/2019 03:39, peteolcott wrote:
>> On 9/12/2019 9:11 PM, David Kleinecke wrote:
>>> On Thursday, September 12, 2019 at 7:00:09 PM UTC-7, peteolcott wrote:
>>>>
>>>> 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].
>>> But there is no first point in the half-open interval
>>> (0.0, 1.0]
>>>
>>
>> THAT IS TOTALLY INCORRECT
>> IT SPECIFIES A LINE SEGMENT OF EXACTLY 1.0 LENGTH.
>>
>> encyclopediaofmath.org/index.php/Interval_and_segment
>>
>> Interval and segment
>> The simplest sets of points on the line. An interval (open interval)
>> is a set of points on a line lying between two fixed points and ,
>> where and themselves are considered not to belong to the interval.
>>
>> (0.0, 1.0] specifies the point immediately adjacent to 0.0
>> and the point 1.0.
>
> No, (0.0, 1.0] =df {x:0.0 < x <= 1.0}
>
It is like I said cats are animals and you said no cats are not animals they are living things.
The above sequence of points defines a line segment with two endpoints.
It may have never been thought of that way before because there was
no way to uniquely identify the left endpoint and the limits of the
expressiveness of language limit what can be conceived.
Now with my new infinitesimal number system copyright 2018, 2019 that
point can be identified as: 0.0[1], so we can understand that a line
segment with two endpoints does exist.
>>
>> [0.0, 1.0] specifies a line segment that is exactly one geometric
>> point longer than 1.0.
>
> No, [0.0, 1.0] =df {x:0.0 <= x <= 1.0}
>>
>> (0.0, ∞] specifies all of the positive numbers.
>
> No, all the positive numbers is (0.0, ∞).
>
>> [-∞, 0.0) specifies all of the negative numbers.
>
> No, all the negative numbers is (-∞, 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 | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 13:09 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <xOKdncFYveV4seDAnZ2dnUU7-UPNnZ2d@giganews.com> |
| In reply to | #458037 |
On 9/14/2019 11:23 AM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/12/2019 8:00 PM, Ben Bacarisse wrote: > <cut loads of stuff you appear to be ignoring...> > >>>> The common notational convention used for intervals make it clear >>>> that the key notion of my system: [immediately adjacent points on >>>> a number line] do exist, and can be uniquely identified. >>> >>> 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. When qualified that 0, and 1 refer to real numbers your statement that there are zero real numbers (or points on a number line) between 0 and 1 is ridiculous. > 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? > > Adjacent points may exist in your made-up number line, but the notation > for intervals does not "make it clear". In fact, it makes the opposite > clear. It is not a straw man. > >> IT IS CLEAR THAT I HAVE BEEN ALWAYS USING REAL ENDPOINTS. > > As did I when I pointed out that adjacent points do not exist. > >> YOUR SWITCH TO INTEGERS IS PRETTY DAMN STUPID. >> DID YOU THINK YOU WOULD GET AWAY WITH THAT? > > This is not C++. The real interval you write as (0.0, 1.0] is written > by mathematicians as (0, 1]. I'm, not going to break this habit because > you think 1 is an integer and 1.0 is a real. > It took me a long time to cut-and-paste this because all of the variables and symbols were images rather than Unicode: https://www.encyclopediaofmath.org/index.php/Interval_and_segment Interval and segment The simplest sets of points on the line. 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. A segment (closed interval) is a set of points between two points A and B, where A and B are included. The terms "interval" and "segment" are also used for the corresponding sets of real numbers: an interval consists of numbers satisfying a < x < b, while a segment consists of those x for which a ≤ x ≤ b. An interval is denoted by (a, b), or ], and a segment by [a, b]. > What's more, you are quite happy to see it that way. You wrote "the > first point in the interval: (3,4]" a few posts ago, and the Wiki > article you quoted does it in all cases of real intervals. I won't call > this lying because it's due to ignorance and a bad memory. > > (Even in computer languages you can't rely on the syntax to know the > type of the value. You probably don't know enough languages to have > come across such things as polymorphic literals.) > >> 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]. > > There is no first point in the interval (0, 1] and that does not change > if you write (0.0, 1.0] or (0.000. 1.000] because they all mean the same > thing. (There are a lot of things that are false that you think are > obviously true.) > I READ YOUR WORDS INCORRECTLY, SORRY !!! I HAD TO READ THEM FIVE TIMES TO GET WHAT YOU ARE REALLY SAYING. I THOUGHT THAT YOU WERE SAYING (0, 1] HAS ZERO ELEMENTS. 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. > If we have a sequence of points [0.0, 1.0] on a number line and we remove the first point (0.0, 1.0] then it is obvious that this second sequence is exactly one geometric point shorter than the first sequence. The difference in length is that we removed the 1.0 point from the first sequence leaving only the point that it was immediately adjacent to. If we try to remove the next geometric point from the beginning of this sequence we cannot only because there are no notational conventions to say this. Some famous philosopher said that language limits thought. Since we just proved that adjacent geometric points exist, then by induction there is always a next adjacent geometric point 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 | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 14:41 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <8a-dnYGpCZXX3-DAnZ2dnUU7-YfNnZ2d@giganews.com> |
| In reply to | #458251 |
On 9/14/2019 2:30 PM, Fred wrote: > On 14/09/2019 20:27, peteolcott wrote: >> On 9/14/2019 1:33 PM, Fred wrote: >>> On 14/09/2019 19:09, peteolcott wrote: >>> >>>> It took me a long time to cut-and-paste this because all of the variables >>>> and symbols were images rather than Unicode: >>> >>> Spend as much time reading and comprehending as you do cutting and pasting, and you might gain some understanding. It's still wrong so your time was wasted. >>> >>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>> Interval and segment >>>> The simplest sets of points on the line. 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. A segment (closed interval) is >>>> a set of points between two points A and B, where A and B are included. The terms "interval" and "segment" are also >>>> used for the corresponding sets of real numbers: an interval consists of numbers satisfying a < x < b, while a >>>> segment consists of those x for which a ≤ x ≤ b. An interval is denoted by (a, b), or ], and a segment by [a, b]. >>> >>> "or ]" makes no sense. >>> >>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>> >>> >>> >> >> The first one is exactly one geometric point shorter than the second one. > > The length of each of them is b - a. The length of a single point is 0. > If the length of a single geometric point was actually zero then the length of every interval would also be zero because 0 * ∞ = 0, therefore the length of a single point on a number line is NOT zero. -- 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 14:08 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <qljhcf$16p$1@dont-email.me> |
| In reply to | #458266 |
On 2019-09-14 1:41 p.m., peteolcott wrote: > On 9/14/2019 2:30 PM, Fred wrote: >> On 14/09/2019 20:27, peteolcott wrote: >>> On 9/14/2019 1:33 PM, Fred wrote: >>>> On 14/09/2019 19:09, peteolcott wrote: >>>> >>>>> It took me a long time to cut-and-paste this because all of the >>>>> variables >>>>> and symbols were images rather than Unicode: >>>> >>>> Spend as much time reading and comprehending as you do cutting and >>>> pasting, and you might gain some understanding. It's still wrong so >>>> your time was wasted. >>>> >>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>> Interval and segment >>>>> The simplest sets of points on the line. 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. A segment (closed interval) is >>>>> a set of points between two points A and B, where A and B are >>>>> included. The terms "interval" and "segment" are also >>>>> used for the corresponding sets of real numbers: an interval >>>>> consists of numbers satisfying a < x < b, while a >>>>> segment consists of those x for which a ≤ x ≤ b. An interval is >>>>> denoted by (a, b), or ], and a segment by [a, b]. >>>> >>>> "or ]" makes no sense. >>>> >>>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>>> >>>> >>>> >>> >>> The first one is exactly one geometric point shorter than the second >>> one. >> >> The length of each of them is b - a. The length of a single point is 0. >> > > If the length of a single geometric point was actually zero then > the length of every interval would also be zero because 0 * ∞ = 0, ∞ is not a number. You can't perform arithmetic on it. > therefore the length of a single point on a number line is NOT zero. A point, by definition, is dimensionless. It has no size. The number of points in any (non-empty) real interval is exactly the same (2^ℵ_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 15:45 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <i7adnQ0um8EczODAnZ2dnUU7-VfNnZ2d@giganews.com> |
| In reply to | #458270 |
On 9/14/2019 3:08 PM, André G. Isaak wrote: > On 2019-09-14 1:41 p.m., peteolcott wrote: >> On 9/14/2019 2:30 PM, Fred wrote: >>> On 14/09/2019 20:27, peteolcott wrote: >>>> On 9/14/2019 1:33 PM, Fred wrote: >>>>> On 14/09/2019 19:09, peteolcott wrote: >>>>> >>>>>> It took me a long time to cut-and-paste this because all of the variables >>>>>> and symbols were images rather than Unicode: >>>>> >>>>> Spend as much time reading and comprehending as you do cutting and pasting, and you might gain some understanding. It's still wrong so your time was wasted. >>>>> >>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>> Interval and segment >>>>>> The simplest sets of points on the line. 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. A segment (closed interval) is >>>>>> a set of points between two points A and B, where A and B are included. The terms "interval" and "segment" are also >>>>>> used for the corresponding sets of real numbers: an interval consists of numbers satisfying a < x < b, while a >>>>>> segment consists of those x for which a ≤ x ≤ b. An interval is denoted by (a, b), or ], and a segment by [a, b]. >>>>> >>>>> "or ]" makes no sense. >>>>> >>>>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>>>> >>>>> >>>>> >>>> >>>> The first one is exactly one geometric point shorter than the second one. >>> >>> The length of each of them is b - a. The length of a single point is 0. >>> >> >> If the length of a single geometric point was actually zero then >> the length of every interval would also be zero because 0 * ∞ = 0, > > ∞ is not a number. You can't perform arithmetic on it. > >> therefore the length of a single point on a number line is NOT zero. > > A point, by definition, is dimensionless. It has no size. > > The number of points in any (non-empty) real interval is exactly the same (2^ℵ_0). > > André > > That is contradicted by the fact that the interval (0.0, 1.0] has exactly one more geometric point than the interval (0.0, 1.0). The common wisdom that a geometric point has zero width is now proven to be incorrect. More accurately a single geometric point has infinitesimal width. -- 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 16:06 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <of6dnTFRafbfy-DAnZ2dnUU7-SednZ2d@giganews.com> |
| In reply to | #458274 |
On 9/14/2019 3:55 PM, Fred wrote: > On 14/09/2019 21:45, peteolcott wrote: > > >> The common wisdom that a geometric point has zero width is now >> proven to be incorrect. More accurately a single geometric >> point has infinitesimal width. > > The common wisdom, as you call it, is indeed wise. He who says that a single geometric point has infinitesimal width is only making a useful statement if it is accompanied by a theory of infinitesimals. Luckily, there are theories of infinitesimals (see > here https://en.wikipedia.org/wiki/Infinitesimal#Number_systems_that_include_infinitesimals for starters). Is any of them yours? If not, where may a coherent account of yours be found? > > Who else has proved that cardinality is incorrect? -- 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 19:24 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <wvSdnW-vtIUDGeDAnZ2dnUU7-bvNnZ2d@giganews.com> |
| In reply to | #458251 |
On 9/14/2019 6:47 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/14/2019 11:23 AM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> 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]. >>> >>> There is no first point in the interval (0, 1] and that does not change >>> if you write (0.0, 1.0] or (0.000. 1.000] because they all mean the same >>> thing. (There are a lot of things that are false that you think are >>> obviously true.) >>> >> >> I READ YOUR WORDS INCORRECTLY, SORRY !!! > > OK. > >> 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. >> >> If we have a sequence of points [0.0, 1.0] on a number line and we remove >> the first point (0.0, 1.0] then it is obvious that this second sequence is >> exactly one geometric point shorter than the first sequence. > > The usual measure on intervals makes [0, 1] and (0, 1] the same length > so you need to say PO-shorter, and then define what you mean by that. > But this is a side issue. > That is defining X = X + 1. The first interval contains 1.0, the second interval does not contain 1.0. >> The difference in length is that we removed the 1.0 point from the first >> sequence leaving only the point that it was immediately adjacent to. > > That there is a first point in [0, 1] is not in dispute. > >> If we try to remove the next geometric point from the beginning of >> this sequence we cannot only because there are no notational >> conventions to say this. Some famous philosopher said that language >> limits thought. > > No, you were able to express the thought perfectly well. You talked > about "the point immediately adjacent to" 0. That is perfectly clear, > and denotes something that does not exist. > It is self evidently the first point of this interval: (0.0, 1.0) > You can't do impossible things just by inventing notions for them. The above interval DOES HAVE A FIRST POINT. This point is the point immediately after 0.0. We cannot say that it does not exist ONLY BECAUSE EXISTING NUMBER SYSTEMS CANNOT EXPRESS IT. > There is no number adjacent to 0, even if you say it's called 0[1]. We know that there are a contiguous set of points between (0.0, 1.0] If we remove the last one then one of them the sequence is infinitesimally less than 1.0 long. > > You /can/ invent a set of objects of the form r[k] (provided you are > prepared to work harder at defining them you seem prepared to be), but > no one will care about them unless you can show them to be interesting > in some way (and that's /way/ more work than you are prepared to do). > As it stands it refutes cardinality. >> Since we just proved that adjacent geometric points exist, then by >> induction there is always a next adjacent geometric point on the >> number line. > > You don't know what a proof is if you think you have proved anything. > -- 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 21:33 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <c4OdneqApdJuP-DAnZ2dnUU7-YfNnZ2d@giganews.com> |
| In reply to | #458285 |
On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>> No. The common notational convention used for intervals shows that
>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>> you can't remove the first and second.
>>>>
>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>> exactly one geometric point shorter than the first sequence.
>>>
>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>> so you need to say PO-shorter, and then define what you mean by that.
>>> But this is a side issue.
>>
>> That is defining X = X + 1.
>
> No it isn't. It is defining length(X) = length(X U {0}) and this is
> indeed the usual definition when both X and X U {0} are intervals.
> Making an open interval closed does no change the length.
>
(0, 1] versus (0, 1) as a range of whole %
The first one is 0% to 100%
The second one is 0% to 99%
You can't magically ignore an actual difference just because it is infinitesimal.
(0, 1] a length of exactly 1.0
(0, 1) a length infinitesimally shorter than 1.0.
--
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 22:40 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <T6idnb9L9ZxeL-DAnZ2dnUU7-XHNnZ2d@giganews.com> |
| In reply to | #458293 |
On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>> you can't remove the first and second.
>>>>>>
>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>
>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>> But this is a side issue.
>>>>
>>>> That is defining X = X + 1.
>>>
>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>> indeed the usual definition when both X and X U {0} are intervals.
>>> Making an open interval closed does no change the length.
>>
>> (0, 1] versus (0, 1) as a range of whole %
>> The first one is 0% to 100%
>> The second one is 0% to 99%
>
> No, that would be (0, 0.99) (or [0, 0.99]).
There are too many ways to correctly say this.
(0, 100] integers is 0 to 100
(0, 100) integers is 0 to 99
>
>> You can't magically ignore an actual difference just because it is infinitesimal.
>> (0, 1] a length of exactly 1.0
>> (0, 1) a length infinitesimally shorter than 1.0.
>
> It's not magic. Length is defined that way for a reason. As I have
> said time and time again, just call your notion PO-length, define it
> properly, and we can decide if we care about it or not.
>
0.0 to 100.0 including the 100 is 0 to 100.0
0.0 to 100.0 not including the 100 is 0 to 99.999999999999999999999999999999999999999... on to infinity
--
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 22:40 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qlkfbo$4iq$1@dont-email.me> |
| In reply to | #458303 |
On 2019-09-14 9:40 p.m., peteolcott wrote:
> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>> adjacent points do not exist. While [0, 1] has a least member,
>>>>>>>> (0, 1]
>>>>>>>> does not. You can remove the first number in [0, 1] to get (0,
>>>>>>>> 1] but
>>>>>>>> you can't remove the first and second.
>>>>>>>
>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and
>>>>>>> we remove
>>>>>>> the first point (0.0, 1.0] then it is obvious that this second
>>>>>>> sequence is
>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>
>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same
>>>>>> length
>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>> But this is a side issue.
>>>>>
>>>>> That is defining X = X + 1.
>>>>
>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>> Making an open interval closed does no change the length.
>>>
>>> (0, 1] versus (0, 1) as a range of whole %
>>> The first one is 0% to 100%
>>> The second one is 0% to 99%
>>
>> No, that would be (0, 0.99) (or [0, 0.99]).
>
> There are too many ways to correctly say this.
> (0, 100] integers is 0 to 100
> (0, 100) integers is 0 to 99
>
>>
>>> You can't magically ignore an actual difference just because it is
>>> infinitesimal.
>>> (0, 1] a length of exactly 1.0
>>> (0, 1) a length infinitesimally shorter than 1.0.
>>
>> It's not magic. Length is defined that way for a reason. As I have
>> said time and time again, just call your notion PO-length, define it
>> properly, and we can decide if we care about it or not.
>>
>
> 0.0 to 100.0 including the 100 is 0 to 100.0
> 0.0 to 100.0 not including the 100 is 0 to
> 99.999999999999999999999999999999999999999... on to infinity
Which is equal to exactly 1. The misconception that these two numbers
are different is sufficiently commonplace that it gets its own wikipedia
page.
<https://en.wikipedia.org/wiki/0.999...>
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 10:17 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <4bmdnZCR0LAZOuLAnZ2dnUU7-RfNnZ2d@giganews.com> |
| In reply to | #458303 |
On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>> you can't remove the first and second.
>>>>>>>>
>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>
>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>> But this is a side issue.
>>>>>>
>>>>>> That is defining X = X + 1.
>>>>>
>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>> Making an open interval closed does no change the length.
>>>>
>>>> (0, 1] versus (0, 1) as a range of whole %
>>>> The first one is 0% to 100%
>>>> The second one is 0% to 99%
>>>
>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>
>> There are too many ways to correctly say this.
>> (0, 100] integers is 0 to 100
>> (0, 100) integers is 0 to 99
>
> No. Sadly, almost everything you post introduces new errors. There are
> no open intervals in the integers so using the () notation is silly.
>
> You can, of course, give it a meaning (as you have tried to do here) but
> even then you get it wrong. If the "open" end means the bound is
> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>
> Why switch to integers which have totally different properties?
>
>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>> (0, 1] a length of exactly 1.0
>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>
>>> It's not magic. Length is defined that way for a reason. As I have
>>> said time and time again, just call your notion PO-length, define it
>>> properly, and we can decide if we care about it or not.
>>>
>>
>> 0.0 to 100.0 including the 100 is 0 to 100.0
>> 0.0 to 100.0 not including the 100 is 0 to
>> 99.999999999999999999999999999999999999999... on to infinity
>
> I propose Ben's law: Every sufficiently long mathematical crank thread
> ends up "debating" whether 0.999... = 1 or not.
>
> No. 99.999... = 100 and you stated that 100 is not included.
>
> There is no notation for the largest real in the open interval (0, 100),
> not because no one has come up with a notation for it (that's trivial,
> but the words will do) but because there is no such number.
>
Do you realize that you just said that the number line is defined with gaps?
There is either a contiguous set of points between 0 and 100 or there are
gaps between 0 and 100, those are the only two choices.
> This fact follows trivially from the definition of an open set in a
> metric space, or from the axioms of the reals, or from the first baby
> steps in topology... Repeatedly referring to a provably non-existent
> object is just silly.
>
https://www.encyclopediaofmath.org/index.php/Interval_and_segment
An interval (open interval) is a set of points on a line lying between two fixed
points A and B, where A and B themselves are considered not to belong to the interval.
This means that there is a first point and there is a last point of every
open interval. (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
(0,3] specifies a length of that is exactly one geometric point less than this [0,3].
Interpreted as integers
(0,3] specifies {1,2,3}
[0,3] specifies {0,1,2,3} which is 1.0 longer
--
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 09:26 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qlo9jg$i6d$1@dont-email.me> |
| In reply to | #458433 |
On 2019-09-16 9:17 a.m., peteolcott wrote:
> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>
>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>> No. The common notational convention used for intervals shows
>>>>>>>>>> that
>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least
>>>>>>>>>> member, (0, 1]
>>>>>>>>>> does not. You can remove the first number in [0, 1] to get
>>>>>>>>>> (0, 1] but
>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>
>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and
>>>>>>>>> we remove
>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second
>>>>>>>>> sequence is
>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>
>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same
>>>>>>>> length
>>>>>>>> so you need to say PO-shorter, and then define what you mean by
>>>>>>>> that.
>>>>>>>> But this is a side issue.
>>>>>>>
>>>>>>> That is defining X = X + 1.
>>>>>>
>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>> Making an open interval closed does no change the length.
>>>>>
>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>> The first one is 0% to 100%
>>>>> The second one is 0% to 99%
>>>>
>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>
>>> There are too many ways to correctly say this.
>>> (0, 100] integers is 0 to 100
>>> (0, 100) integers is 0 to 99
>>
>> No. Sadly, almost everything you post introduces new errors. There are
>> no open intervals in the integers so using the () notation is silly.
>>
>> You can, of course, give it a meaning (as you have tried to do here) but
>> even then you get it wrong. If the "open" end means the bound is
>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>
>> Why switch to integers which have totally different properties?
>>
>>>>> You can't magically ignore an actual difference just because it is
>>>>> infinitesimal.
>>>>> (0, 1] a length of exactly 1.0
>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>
>>>> It's not magic. Length is defined that way for a reason. As I have
>>>> said time and time again, just call your notion PO-length, define it
>>>> properly, and we can decide if we care about it or not.
>>>>
>>>
>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>> 0.0 to 100.0 not including the 100 is 0 to
>>> 99.999999999999999999999999999999999999999... on to infinity
>>
>> I propose Ben's law: Every sufficiently long mathematical crank thread
>> ends up "debating" whether 0.999... = 1 or not.
>>
>> No. 99.999... = 100 and you stated that 100 is not included.
>>
>> There is no notation for the largest real in the open interval (0, 100),
>> not because no one has come up with a notation for it (that's trivial,
>> but the words will do) but because there is no such number.
>>
>
> Do you realize that you just said that the number line is defined with
> gaps?
> There is either a contiguous set of points between 0 and 100 or there are
> gaps between 0 and 100, those are the only two choices.
No. You are describing a number line with gaps. He is not. If there were
indeed some largest real in the interval (0,100) (let's call it L), then
what number lies between L and 100? According to you, none. But, it is
axiomatic that for the real numbers, for every x and every y if z < y
then there exists some z such that x < z < y. This proves (by reductio
ad absurdum) that there is no such number L.
André
--
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 10:36 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <P9Kdnd8KC4x1NuLAnZ2dnUU7-XfNnZ2d@giganews.com> |
| In reply to | #458435 |
On 9/16/2019 10:26 AM, André G. Isaak wrote:
> On 2019-09-16 9:17 a.m., peteolcott wrote:
>> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>
>>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>>
>>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>>
>>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>>>> But this is a side issue.
>>>>>>>>
>>>>>>>> That is defining X = X + 1.
>>>>>>>
>>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>>> Making an open interval closed does no change the length.
>>>>>>
>>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>>> The first one is 0% to 100%
>>>>>> The second one is 0% to 99%
>>>>>
>>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>>
>>>> There are too many ways to correctly say this.
>>>> (0, 100] integers is 0 to 100
>>>> (0, 100) integers is 0 to 99
>>>
>>> No. Sadly, almost everything you post introduces new errors. There are
>>> no open intervals in the integers so using the () notation is silly.
>>>
>>> You can, of course, give it a meaning (as you have tried to do here) but
>>> even then you get it wrong. If the "open" end means the bound is
>>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>>
>>> Why switch to integers which have totally different properties?
>>>
>>>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>>>> (0, 1] a length of exactly 1.0
>>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>>
>>>>> It's not magic. Length is defined that way for a reason. As I have
>>>>> said time and time again, just call your notion PO-length, define it
>>>>> properly, and we can decide if we care about it or not.
>>>>>
>>>>
>>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>>> 0.0 to 100.0 not including the 100 is 0 to
>>>> 99.999999999999999999999999999999999999999... on to infinity
>>>
>>> I propose Ben's law: Every sufficiently long mathematical crank thread
>>> ends up "debating" whether 0.999... = 1 or not.
>>>
>>> No. 99.999... = 100 and you stated that 100 is not included.
>>>
>>> There is no notation for the largest real in the open interval (0, 100),
>>> not because no one has come up with a notation for it (that's trivial,
>>> but the words will do) but because there is no such number.
>>>
>>
>> Do you realize that you just said that the number line is defined with gaps?
>> There is either a contiguous set of points between 0 and 100 or there are
>> gaps between 0 and 100, those are the only two choices.
>
>
> No. You are describing a number line with gaps. He is not. If there were indeed some largest real in the interval (0,100) (let's call it L), then what number lies between L and 100? According to you, none. But, it is axiomatic that for the real numbers,
> for every x and every y if z < y then there exists some z such that x < z < y. This proves (by reductio ad absurdum) that there is no such number L.
>
> André
>
>
Since it is clear that (0,100) specifies every geometric point on the number
line between 0 and 100 except for 0 and 100 then it does specify the geometric
point immediately after 0 and the geometric point immediately before 100 with
no geometric points in-between.
If these geometric points are defined to be real numbers and real numbers
are defined to always be divisible by 2, then something about the way that
these things are defined is inherently inconsistent.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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