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Groups > sci.logic > #210463 > unrolled thread
| Started by | peteolcott <Here@Home> |
|---|---|
| First post | 2019-09-11 12:05 -0500 |
| Last post | 2019-09-11 23:15 -0500 |
| Articles | 20 on this page of 322 — 13 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 (cardinality is incorrect) Fred <Fred@nowhere.invalid> - 2019-09-11 18:37 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-12 01:15 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 19:30 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) temakoutera62@gmail.com - 2019-09-11 17:32 -0700
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 01:38 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 01:49 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) George Greene <greeneg@email.unc.edu> - 2019-09-14 18:22 -0700
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-15 02:32 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:19 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 03:29 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 21:41 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:19 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 22:46 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 13:02 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 00:21 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 02:10 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-16 20:41 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 03:34 +0100
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 (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:27 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:26 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-17 11:53 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 03:55 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-18 20:25 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-19 16:35 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:35 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 16:46 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 11:42 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 17:58 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 12:43 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 19:34 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 19:42 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 18:16 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-18 18:12 +0100
Re: Provably unprovable eliminates incompleteness (NO GAPS) peteolcott <Here@Home> - 2019-09-19 10:24 -0500
Re: Provably unprovable eliminates incompleteness (NO GAPS) Fred <Fred@nowhere.invalid> - 2019-09-19 16:39 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 18:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-17 20:41 -0700
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 05:15 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 18:42 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-18 12:58 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 19:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 01:42 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-18 20:46 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-19 02:52 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-19 22:24 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 17:13 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 01:05 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 19:49 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 02:34 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-19 20:54 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 03:32 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-20 14:16 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-20 17:49 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-20 07:16 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-20 21:37 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-20 15:53 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-21 00:10 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 09:45 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-21 17:20 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Jim Burns <james.g.burns@att.net> - 2019-09-21 14:39 -0400
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-22 13:32 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-23 19:50 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-24 02:27 +0100
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-24 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) peteolcott <Here@Home> - 2019-09-21 15:22 -0500
Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) Fred <Fred@nowhere.invalid> - 2019-09-18 18:02 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:10 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-17 09:06 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-14 22:54 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-15 12:06 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 01:42 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 02:50 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 04:07 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 04:20 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-11 22:22 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-12 16:33 +0100
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) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-13 02:00 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-12 21:39 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben Fred <Fred@nowhere.invalid> - 2019-09-13 16:38 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben peteolcott <Here@Home> - 2019-09-13 11:48 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben Fred <Fred@nowhere.invalid> - 2019-09-13 17:54 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 00:51 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 17:23 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 13:09 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 19:28 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 19:33 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 14:27 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 20:30 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 14:41 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 13:02 -0700
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 Fred <Fred@nowhere.invalid> - 2019-09-14 21:18 +0100
Re: Cantor was wrong about cardinality --- APOLOGY André G. Isaak <agisaak@gm.invalid> - 2019-09-14 14:25 -0600
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:03 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:19 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 15:45 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 21:55 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:06 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:20 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 00:54 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Exfalso Quodlibet <exflaso.quodlibet@gmail.com> - 2019-09-14 14:07 -0700
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 21:14 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 16:01 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-14 22:17 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 00:47 +0100
Re: Cantor was wrong about cardinality --- APOLOGY peteolcott <Here@Home> - 2019-09-14 19:24 -0500
Re: Cantor was wrong about cardinality --- APOLOGY Fred <Fred@nowhere.invalid> - 2019-09-15 02:20 +0100
Re: Cantor was wrong about cardinality --- APOLOGY Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:43 +0100
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? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:09 +0100
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? Fred <Fred@nowhere.invalid> - 2019-09-15 12:05 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 12:33 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-16 16:50 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 16:55 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-16 20:28 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-16 21:02 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-17 08:16 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-17 08:21 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 15:46 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 18:07 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Me <invalid@invalid.de> - 2019-09-17 01:09 +0200
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2019-09-17 02:33 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently peteolcott <Here@Home> - 2019-09-16 20:53 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:55 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 19:21 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently André G. Isaak <agisaak@gm.invalid> - 2019-09-16 21:40 -0600
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Keith Thompson <kst-u@mib.org> - 2019-09-16 21:38 -0700
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 00:24 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). peteolcott <Here@Home> - 2019-09-17 11:39 -0500
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently (some concurrence). Fred <Fred@nowhere.invalid> - 2019-09-17 17:55 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-17 08:36 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-17 17:31 +0100
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 --- (Correction) Fred <Fred@nowhere.invalid> - 2019-09-17 20:33 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-17 20:29 +0100
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 Fred <Fred@nowhere.invalid> - 2019-09-18 17:55 +0100
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 --- Reals are defined inconsistently Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 04:36 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:27 +0100
Re: Cantor was wrong about cardinality --- (Mike Terry Concurrence ] peteolcott <Here@Home> - 2019-09-19 11:46 -0500
Re: Cantor was wrong about cardinality --- (Mike Terry Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:00 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-17 08:23 +0100
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 ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:09 +0100
Re: Cantor was wrong about cardinality --- [ Keith Thompson Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-19 18:22 +0100
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 --- [ Keith Thompson Concurrence ] Fred <Fred@nowhere.invalid> - 2019-09-20 14:11 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 19:47 +0100
Re: Cantor was wrong about cardinality --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 18:16 +0100
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 --- Reals are defined inconsistently Fred <Fred@nowhere.invalid> - 2019-09-16 18:08 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 01:49 +0100
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? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 03:25 +0100
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? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 14:26 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? peteolcott <Here@Home> - 2019-09-17 11:55 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Python <python@invalid> - 2019-09-17 18:59 +0200
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 04:01 +0100
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? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-18 05:19 +0100
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 --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 23:09 +0100
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 23:02 +0100
Re: Cantor was wrong about cardinality --- [ CONCURRENCE ] peteolcott <Here@Home> - 2019-09-18 11:10 -0500
Re: Cantor was wrong about cardinality --- APOLOGY clear yet? Fred <Fred@nowhere.invalid> - 2019-09-18 18:39 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 12:15 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-12 10:37 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 16:56 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:27 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 16:43 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:51 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 18:12 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-14 22:54 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:28 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 11:34 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-14 18:05 +0100
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 Goofed) Fred <Fred@nowhere.invalid> - 2019-09-15 02:04 +0100
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 (Andy really did Goof) Fred <Fred@nowhere.invalid> - 2019-09-16 16:15 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 01:26 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 19:32 -0500
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 19:36 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 02:26 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 02:54 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 21:38 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 04:14 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-14 22:45 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-15 12:53 +0100
Re: Cantor was wrong about cardinality --- COMPLETE peteolcott <Here@Home> - 2019-09-16 10:21 -0500
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-16 16:27 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-17 00:35 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 11:53 +0100
Re: Cantor was wrong about cardinality --- COMPLETE Fred <Fred@nowhere.invalid> - 2019-09-15 02:22 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-12 17:04 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 00:10 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-12 23:16 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 10:09 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 09:41 -0600
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:36 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) André G. Isaak <agisaak@gm.invalid> - 2019-09-13 11:14 -0600
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) Fred <Fred@nowhere.invalid> - 2019-09-13 19:08 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-14 22:49 +0100
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) Fred <Fred@nowhere.invalid> - 2019-09-13 16:45 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Fred <Fred@nowhere.invalid> - 2019-09-13 16:57 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-13 11:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 02:30 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) peteolcott <Here@Home> - 2019-09-14 00:53 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-14 00:55 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) BEN LIED !!! peteolcott <Here@Home> - 2019-09-17 11:33 -0500
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-09-14 17:14 +0100
Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) George Greene <greeneg@email.unc.edu> - 2019-09-14 18:24 -0700
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) Fred <Fred@nowhere.invalid> - 2019-09-15 11:50 +0100
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) George Greene <greeneg@email.unc.edu> - 2019-09-11 20:55 -0700
Re: Provably unprovable eliminates incompleteness (cardinality is incorrect) peteolcott <Here@Home> - 2019-09-11 23:15 -0500
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-24 02:27 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87mueusctn.fsf@bsb.me.uk> |
| In reply to | #211222 |
peteolcott <Here@Home> writes: > On 9/22/2019 7:32 AM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> <cut> >>> There are no reals in this sequence: 0.0[1 to ∞] >> >> I am glad you see that now. >> >>> (0.0, 1.0] is one point longer than (0.0, 1.0). >> >> (0.0, 1.0] includes one point that is not in (0.0, 1.0) but the length >> of (0.0, 1.0] and (0.0, 1.0) is the same. You can fix your claim by >> talking about the PO-length of an interval, and you can avoid being >> wrong about PO-length by continuing not to define it. >> > > The first interval is clearly infinitesimally longer than the second. It will be clearly PO-longer just as soon as you define what PO-length is. You won't currently say (not are you likely to ever say). > That no one else agrees is of no consequence. Every one already agrees that you can have your own private meaning for length. You can call the sky PO-red for all anyone cares. Bit in the context of real intervals, length has a definition you can't reject without consequences. One consequence is that you will look silly. >>> Infinitesimals fill in the gaps between Reals, they have no bijection >>> to Reals. >> >> Sets that don't biject with the reals (not the Reals) are, of course, >> very common and don't contradict anything Cantor wrote. >> >> I'm absolutely sure you don't mean what the words you said mean, but I >> can't go telling you what you are trying to say. Sets that have no >> bijection with R either have fewer members (to use a colloquial phrase) >> like N, Z and Q, or they have more like P(R) or R->R. >> >>> A single point on the number line can be thought of as having a length somewhat >>> comparable to 1.0/∞. >>> >>> Everything that I said above supersedes and replaces everything else >>> that I said. >> >> So you are now only making four claims: >> >> * the first of which everyone but you has known from that start; >> >> * the second of which is wrong; >> >> * the third of which is a trivial statement that, if it relates to >> Cantor's theorem at all, backs it up; and >> >> * the fourth of which is some vague waffle about the how the length of >> a point "can be" (not even "should be") "thought of" (not "is") >> "somewhat" (you don't say to what extent) "comparable to" (just a >> vague bit like) something you have not defined. >> >> That last remark is vague beyond the wildest dreams of many Usenet >> cranks. I think you are getting the hang of this! I shall assume you agree that these are your only extant claims. Pretty dull really, aren't they? -- Ben.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-24 15:22 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <bMSdnTFWhf5l5xfAnZ2dnUU7-THNnZ2d@giganews.com> |
| In reply to | #211223 |
On 9/23/2019 8:27 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/22/2019 7:32 AM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> <cut> >>>> There are no reals in this sequence: 0.0[1 to ∞] >>> >>> I am glad you see that now. >>> >>>> (0.0, 1.0] is one point longer than (0.0, 1.0). >>> >>> (0.0, 1.0] includes one point that is not in (0.0, 1.0) but the length >>> of (0.0, 1.0] and (0.0, 1.0) is the same. You can fix your claim by >>> talking about the PO-length of an interval, and you can avoid being >>> wrong about PO-length by continuing not to define it. >>> >> >> The first interval is clearly infinitesimally longer than the second. > > It will be clearly PO-longer just as soon as you define what PO-length > is. You won't currently say (not are you likely to ever say). > 1.0 / ∞ is the width of one point on the number line. >>>> (0.0, 1.0] is one point longer than (0.0, 1.0). To say that the length of the two intervals is identical is to say that the intervals themselves are identical because they only vary in infinitesimal length. >> That no one else agrees is of no consequence. > > Every one already agrees that you can have your own private meaning for > length. You can call the sky PO-red for all anyone cares. Bit in the > context of real intervals, length has a definition you can't reject > without consequences. One consequence is that you will look silly. > I augment prior incomplete understanding. To the rest of the world claiming spherical Earth at one time seemed to be stupidly incorrect. >>>> Infinitesimals fill in the gaps between Reals, they have no bijection >>>> to Reals. >>> >>> Sets that don't biject with the reals (not the Reals) are, of course, >>> very common and don't contradict anything Cantor wrote. >>> >>> I'm absolutely sure you don't mean what the words you said mean, but I >>> can't go telling you what you are trying to say. Sets that have no >>> bijection with R either have fewer members (to use a colloquial phrase) >>> like N, Z and Q, or they have more like P(R) or R->R. >>> >>>> A single point on the number line can be thought of as having a length somewhat >>>> comparable to 1.0/∞. >>>> >>>> Everything that I said above supersedes and replaces everything else >>>> that I said. >>> >>> So you are now only making four claims: >>> >>> * the first of which everyone but you has known from that start; >>> >>> * the second of which is wrong; >>> >>> * the third of which is a trivial statement that, if it relates to >>> Cantor's theorem at all, backs it up; and >>> >>> * the fourth of which is some vague waffle about the how the length of >>> a point "can be" (not even "should be") "thought of" (not "is") >>> "somewhat" (you don't say to what extent) "comparable to" (just a >>> vague bit like) something you have not defined. >>> >>> That last remark is vague beyond the wildest dreams of many Usenet >>> cranks. I think you are getting the hang of this! > > I shall assume you agree that these are your only extant claims. Pretty > dull really, aren't they? > -- 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 | 2019-09-21 15:22 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <WPKdnX-fIbkSGxvAnZ2dnUU7-dXNnZ2d@giganews.com> |
| In reply to | #211103 |
On 9/21/2019 5:13 AM, Andy Walker wrote: > On 20/09/2019 12:55, Ben Bacarisse wrote: > [Me, in response to DK:] >>> Step by step! As there are [at least] a countable infinity >>> of [conventional] real numbers, what it means is that there is a >>> rather simple bijection between the PO-points [a countable infinity >>> per real] and the reals, >> Really? Has he actually stated that the "Real_Part" can be any real >> number? At least when he replied to my question about that he did not >> say so. His reply was >> | Any identifiable number can go into the "real" part. >> which is nothing if not classic crank -- it introduces new undefined >> term and uses scare quotes to suggest that the real part is not really >> for what the world calls real numbers. Depending on what an >> identifiable number is, it may turn out that the PO-points r[k] are >> indeed countable. > > I think we're well beyond PO's pay grade. Given his views on > the HP and on diagonal proofs, my suspicion is that he recognises only > the computable reals. This is because the standard example of an > uncomputable real is one whose nth digit is some representation of > the halting state of the nth TM, eg when run with an empty tape; and > in PO-land that is [no doubt] computable. So "identifiable" means > "computable", and any other real number would be "empty rhetoric > devoid blah-de-blah", on which he "calls BS". > >> Putting that aside, he's made the rookie crank mistake of being clear >> about some other things. For example: >> "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" >> and >> "the number line does include every Real number". >> So we don't need any "base" other than 0, but he's also said that there >> are no reals between any 0[k] and 0[k+1] and, because he's also agreed >> that there is no least positive real, none of the 0[k] (for k > 0) can >> be real themselves. It's all a self-contradictory mess. > > Yes; but that has never worried him! He latches on to some > idea, and repeats and develops it as nauseam, without ever thinking > about how it meshes with other parts of maths and computing. If you > try to point out the contradictions, you are just indulging in "empty > rhetoric ..." or "extraneous detail" or whatever. It's also classic > troll behaviour, but my personal belief is that he is not capable of > sustaining that. > > [...] > > [Later:] >> Sorry, I meant to agree with this key point in my reply... >>> ... Pete disputes that there are as many reals as the rest >>> of us believe; PO-points neither advance nor retard that disputation. >>> Apart from filling Pete's need to have no gaps in his imagined world, >>> and apart from making arithmetic impossible in general, PO-points are >>> an irrelevance. >> Yes, any bijection between N and PO-points could be made better (and >> simpler) just by throwing out all the extra points to leave a bijection >> between N and R! > > True, but that's a different point [and there is indeed a > (non-computable!) bijection between N and the computable reals]. > Mine was that whether R is countable or uncountable doesn't affect > the existence of a bijection between R and R-together-with-a- > countable-infinity-of-infinitesimals. Only if R is finite do > infinitesimals change that. But that would be rather an extreme > view of the reals! > The distance between zero and the point on the number line immediately after zero Number M = 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 | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-18 18:02 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qltnul$8uu$1@news.albasani.net> |
| In reply to | #210972 |
On 18/09/2019 04:19, peteolcott wrote:
> Mike Terry agreed with this verbatim: [A, B] - {A} = (A, B]
Anyone will agree with it. It's well-known notation.
> Infinitesimal Numbers would encode (A, B] as [A[1], B]
That is an abuse of notion. [x,y] ought to be a closed interval. If
you are defining [A[1], B] to be (A, B], then it no longer is.
> We merely extrapolate the very next elaboration
> [A[1], B] - {A[1]} = (A[1], B] encoded as [A[2], B]
Having introduced a poor notation, you now allow yourself to be mislead
by it - there is no set {A[1]}.
> This shows how Infinitesimal Numbers directly reference immediately
> adjacent points on a number line.
>
> 0.0[0] = 0.0
> 0.0[1] = the next point after 0.0
Just because you can write the words doesn't mean they denote anything.
> 0.0[2] = 2 points after 0.0
> 0.0[3] = 3 points after 0.0
>
>
>
>
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-17 09:10 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlq4ee$t48$1@news.albasani.net> |
| In reply to | #210866 |
On 17/09/2019 02:41, peteolcott wrote:
> On 9/16/2019 8:10 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/16/2019 6:21 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>> <cut>
>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment
>>>>> An interval (open interval) is a set of points on a line lying between
>>>>> two fixed points A and B, where A and B themselves are considered not
>>>>> to belong to the interval.
>>>>>
>>>>> This clearly specifies that there is a point immediately after A and
>>>>> before B.
>>>>
>>>> No it doesn't. I don't think there is any way forward here because you
>>>> are simply reading things into that text that are not there. Normally
>>>> I'd suggest you go and read about the development of the reals, but
>>>> that's a non-starter for you.
>>>
>>> When we remove the beginning 0.5 from [0.0, 2.0] we derive [0.5, 2.0]
>>> with a first point of 0.5.
>>
>> You could be clearer, but you are not wrong:
>>
>> [0, 2] \ [0, 0.5) = [0.5, 2] with first point 0.5
>>
>> but
>>
>> [0, 2] \ [0, 0.5] = (0.5, 2] with no first point.
>>
>
> You keep getting confused by this.
> [0, 2] and we remove the very first point (0, 2]
> then necessarily all of the rest of the points remain.
>
> Just because we don't have a real number to express the
> first point does not prove that there is no first point
> as everyone assumes.
[0,2] =df {x:0 <= x <= 2} is a set of real numbers and nothing else. So
if a point or interval is removed from it, all that can remain are real
numbers. (I also think you're confusing "number" and "numeral".)
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-17 09:06 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlq46a$v0p$1@news.albasani.net> |
| In reply to | #210857 |
On 17/09/2019 00:24, peteolcott wrote: > When we remove the beginning 0.5 from [0.0, 2.0] Completely obscure! You seem to mean When we remove the first quarter of [0.0, 2.0]... or When we remove [0, 0.5) from [0.0, 2.0]... The second being better because "the first quarter" might be [0, 0.5) or [0, 0.5]. The notation (for so-called set subtraction) is A\B. A\B is the set of elements of A that are not in B. > we derive [0.5, 2.0] > with a first point of 0.5.
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-14 22:54 -0600 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qlkg5g$7h9$1@dont-email.me> |
| In reply to | #210734 |
On 2019-09-14 8:41 p.m., peteolcott wrote: > On 9/14/2019 9:29 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/14/2019 8:22 PM, George Greene wrote: >>>> On Wednesday, September 11, 2019 at 8:30:38 PM UTC-4, peteolcott wrote: >>>>>>> We already know there is a bijection between all of the geometric >>>>>>> points >>>>>>> on a number line and the set of real numbers. >>>> >>>> True. >>> >>> Someone corrected my on this. >>> Some of the numbers on the number line (like PI) are not Real numbers. >> >> What criteria do you use to tell if you should take someone's >> corrections? Because whoever it was got it wrong. pi (if you mean the >> pi we all know and love) is a real number (written with a lower case >> "r".) >> >> In fact, the two correspond exactly. The real numbers are the algebraic >> abstraction of the concept of a continuous unbounded line. >> > > OK great that makes things simpler. I was thinking that irrational numbers > were not real. My correction has been corrected, thanks. If you're not even clear on what the real numbers even are, what makes you think you're in any position to make any substantive claims about them? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-15 12:06 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <qll60g$p8m$2@news.albasani.net> |
| In reply to | #210729 |
On 15/09/2019 03:19, peteolcott wrote: > Some of the numbers on the number line (like PI) are not Real numbers. Do Real numbers differ from real numbers?
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 01:42 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <874l1il4zm.fsf@bsb.me.uk> |
| In reply to | #210486 |
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: >>>> 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. -- Ben.
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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 | #210502 |
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 | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 02:50 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <87mufajnag.fsf@bsb.me.uk> |
| In reply to | #210505 |
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. -- Ben.
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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 | #210508 |
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 | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 04:07 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <87h85ijjps.fsf@bsb.me.uk> |
| In reply to | #210509 |
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. -- Ben.
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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 | #210511 |
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 | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 04:20 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <87blvqjj4s.fsf@bsb.me.uk> |
| In reply to | #210512 |
peteolcott <Here@Home> writes: > 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? You need to be prepared to answer my questions. There's no other way you can learn. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-11 22:22 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <7ZqdnYlowZ5nJOTAnZ2dnUU7-eGdnZ2d@giganews.com> |
| In reply to | #210513 |
On 9/11/2019 10:20 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> 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? > > You need to be prepared to answer my questions. There's no other way > you can learn. > I will answer any good faith questions in good faith. It really seems to me that your good faith answer to my above questions would necessarily prove that I am correct. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-12 16:33 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <875zlxjzqm.fsf@bsb.me.uk> |
| In reply to | #210514 |
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?
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?
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?
Q3. Given two arbitrary points r1[i1] and r2[i2], is r1[i1] = r2[i2] if
and only if r1 = r2 and i1 = i2?
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?
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"?
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?
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.)
> 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.
--
Ben.
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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 | #210542 |
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 | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-13 02:00 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) |
| Message-ID | <87k1adhuwr.fsf@bsb.me.uk> |
| In reply to | #210558 |
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.
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-12 21:39 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (Cantor was wrong about cardinality) Deceptive Strawman by Ben |
| Message-ID | <1PGdnVh-j6TTnObAnZ2dnUU7-VHNnZ2d@giganews.com> |
| In reply to | #210584 |
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. [0.0, 1.0] specifies a line segment that is exactly one geometric point longer than 1.0. (0.0, ∞] specifies all of the positive numbers. [-∞, 0.0) specifies all of the negative numbers. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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