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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 | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-18 20:46 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <45OdnVfDl4hzQB_AnZ2dnUU7-XfNnZ2d@giganews.com> |
| In reply to | #211056 |
On 9/18/2019 7:42 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/18/2019 12:42 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> Sure it does because other number systems cannot account for ALL >>>> of the points on the number line. >>> >>> Cantor proved the real are uncountable. The theorem stands even if they >>> don't "account for ALL of the points on the number line". The theorem >>> is about the reals. >> >> If Infinitesimals indexed by integers can count ALL of the numbers >> on the number line including the subset of numbers that are Reals >> then Cantor is refuted. > > Of course. In fact if you can do that you can simplify matters by > counting ONLY those that are reals. That's the daft thing: most of your > infinitesimals are just a side show. Throw away all of your > infinitesimals that are not reals and count the result (you can't). > >> That Integers cannot count the Real directly yet can count them >> indirectly does not actually indicate a difference in the "size" of >> the sets, it merely indicates an incompatibility between Reals and >> Integers. > > Well if this waffle means you can can't count the reals, you have not > refuted anything. As long as Integers can count ALL the points on a number line Cantor is refuted. That Reals skip some of these points is self-evident in that when Reals approximate adjacency to 0.0 they always leave a gap of a measurable distance size that is never closed, thus points that are unaccounted for. > By all means show a surjective function from Z to > some set that includes the reals as special cases and I'll publish a > better paper with a direct surjection from N to R. (Neither is > possible, by the way.) > > The astute reader will note that we are still missing the bijection you > claim. Mind you, we are still missing the impossible Turing machine you > claimed to have in December last year, so I'm not holding my breath for > any of this. You never show any of the magic rainbow sparkle ponies you > claim to have. > > <cut> >>>> It is pretty silly to envision any infinite set that is "larger" >>>> than any other infinite set. >>> >>> Ah, the argument from what someone with mental health issues considers >>> silly. That carries no weight with mathematicians. There is no >>> surjective function from N onto R. This is a proved fact. Stop >>> pretending you have the knowledge to even know what this means, let >>> alone refute it. >>> >>> I repeat my offer to show you why you are wrong, but you would have to >>> be prepared to both explain and learn. >> >> You can't show me where I am wrong > > I can show any intelligent person that you are wrong about Cantor's > theorem simply by showing them the proof of Cantor's theorem. And if > you ever publish a claimed surjective function from Z (or any countable > set) to any set the includes the reals, I will show that intelligent > person where you went wrong. And I'll also show them what you've got > wrong about Turning machines it you ever post that impossible TM you've > boasted about having for months and months. > > But you are not prepared to explain yourself and not open to asking > question when you don't understand an explanation. You can't learning > anything problematic that way so I think you are right about my not > being able to to show /you/ where you are wrong. > > For example, I've explained that your picking off points, one by one, in > any order at all from any set that includes the reals can't ever count > that set, but you never even commented on that much less asked any > intelligent questions to find out more. You just don't want to know why > you are wrong. You just want to keep boasting. > >> you can ONLY show that >> a different set of assumptions leads to a different conclusion. > > That's what you've spent most of the last two decades doing: talking > about things using the usual terms (to hook people in) and then, when > pressed, you pretend that you always meant things to be defined how > you'd like them to be. Define PO-truth as just entailment and, poof!, > you get what you want. The PO-numbers can be "based on zero" and > written as 0[k] with k in Z and, poof!, the "numbers" are countable. > It's so incredible shallow, but then being right is not your objective > here, is it? > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-19 02:52 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qlun01$lg7$1@news.albasani.net> |
| In reply to | #211059 |
On 19/09/2019 02:46, peteolcott wrote: > As long as Integers can count ALL the points on a number line Cantor They can't. Btw, the correct spelling is "integers". What proof that they can't have you looked at, and where do you think it went wrong? > is refuted. That Reals skip some of these points is self-evident in > that when Reals approximate adjacency to 0.0 they always leave a gap > of a measurable distance size that is never closed, thus points that > are unaccounted for. If it were so, that would mean that there are more points on the number line than there are reals (note the small "r"). Since the reals are uncountable, the points on the number line must also be uncountable.
[toc] | [prev] | [next] | [standalone]
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-19 22:24 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87h8585690.fsf@bsb.me.uk> |
| In reply to | #211059 |
peteolcott <Here@Home> writes: > On 9/18/2019 7:42 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/18/2019 12:42 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >> <cut> >>>>> Sure it does because other number systems cannot account for ALL >>>>> of the points on the number line. >>>> >>>> Cantor proved the real are uncountable. The theorem stands even if they >>>> don't "account for ALL of the points on the number line". The theorem >>>> is about the reals. >>> >>> If Infinitesimals indexed by integers can count ALL of the numbers >>> on the number line including the subset of numbers that are Reals >>> then Cantor is refuted. >> >> Of course. In fact if you can do that you can simplify matters by >> counting ONLY those that are reals. That's the daft thing: most of your >> infinitesimals are just a side show. Throw away all of your >> infinitesimals that are not reals and count the result (you can't). >> >>> That Integers cannot count the Real directly yet can count them >>> indirectly does not actually indicate a difference in the "size" of >>> the sets, it merely indicates an incompatibility between Reals and >>> Integers. >> >> Well if this waffle means you can can't count the reals, you have not >> refuted anything. > > As long as Integers can count ALL the points on a number line Cantor > is refuted. Not unless "a number line" includes the reals. You duck and dive about this. I specifically asked about it when you briefly suggested you'd like to learn something, and you specifically did not answer with any clarity. And you are still ducking an diving. Show your bijection and I'll make it better and publish it by ignoring your junk infinitesimals to present a bijection from N to R. (You can't, of course, so I won't get to be famous, but I can at least keep calling you out for boasting about having things you can't actually show.) -- Ben.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 17:13 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qIKdneGpdpbgYB7AnZ2dnUU7-Y3NnZ2d@giganews.com> |
| In reply to | #211097 |
On 9/19/2019 4:24 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/18/2019 7:42 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/18/2019 12:42 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> Sure it does because other number systems cannot account for ALL >>>>>> of the points on the number line. >>>>> >>>>> Cantor proved the real are uncountable. The theorem stands even if they >>>>> don't "account for ALL of the points on the number line". The theorem >>>>> is about the reals. >>>> >>>> If Infinitesimals indexed by integers can count ALL of the numbers >>>> on the number line including the subset of numbers that are Reals >>>> then Cantor is refuted. >>> >>> Of course. In fact if you can do that you can simplify matters by >>> counting ONLY those that are reals. That's the daft thing: most of your >>> infinitesimals are just a side show. Throw away all of your >>> infinitesimals that are not reals and count the result (you can't). >>> >>>> That Integers cannot count the Real directly yet can count them >>>> indirectly does not actually indicate a difference in the "size" of >>>> the sets, it merely indicates an incompatibility between Reals and >>>> Integers. >>> >>> Well if this waffle means you can can't count the reals, you have not >>> refuted anything. >> >> As long as Integers can count ALL the points on a number line Cantor >> is refuted. > > Not unless "a number line" includes the reals. You have confusion derived from the conventional way that these things have been defined. Conventionally it is understood that there is a bijection between points on the number line and the set of Reals. Conventionally it has been understood that there is no such thing as points on the number line that are immediately adjacent to each other because Real numbers are always divisible. I have shown that these conventions result in the inconsistency of points on the number line that are not accounted for by Reals. Since there is no Real number immediately adjacent to 0.0 there is always a measurable gap between 0.0 and every element of the set of Real numbers. This gap has points on the number line that are not accounted for by any Real number. So although the number line does include every Real number it also includes the more dense set of Infinitesimal numbers which fill in the gaps left behind by the Reals. > You duck and dive about > this. I specifically asked about it when you briefly suggested you'd > like to learn something, and you specifically did not answer with any > clarity. > > And you are still ducking an diving. Show your bijection and I'll make > it better and publish it by ignoring your junk infinitesimals to present > a bijection from N to R. (You can't, of course, so I won't get to be > famous, but I can at least keep calling you out for boasting about > having things you can't actually show.) > -- 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 | 2019-09-20 01:05 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <875zln6dcv.fsf@bsb.me.uk> |
| In reply to | #211099 |
peteolcott <Here@Home> writes: > On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: <cut> >>> As long as Integers can count ALL the points on a number line Cantor >>> is refuted. >> >> Not unless "a number line" includes the reals. <cut> > So although the number line does include every Real number it also > includes the more dense set of Infinitesimal numbers which fill in > the gaps left behind by the Reals. An answer! Just in case you are in an answering mood I'll try another: 0[1] is the first PO-point (and not a real) after 0. There are no real points (I'll just call them reals) between 0 and 0[1]. The next point on the number line (according to more than one post I've seen) is 0[2]. Are there any reals between 0[1] and 0[2]? If so, how many? If not, are there any between 0[2] and 0[3]? If so how many? If not, are there any between 0[3] and 0[4]? Can you see where this is going? Can you answer? By the way, it's fine to say you don't know. If you don't know, please don't guess or bluff. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 19:49 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <ZMmdnS2YxpCNvxnAnZ2dnUU7-SHNnZ2d@giganews.com> |
| In reply to | #211101 |
On 9/19/2019 7:05 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> As long as Integers can count ALL the points on a number line Cantor >>>> is refuted. >>> >>> Not unless "a number line" includes the reals. > <cut> >> So although the number line does include every Real number it also >> includes the more dense set of Infinitesimal numbers which fill in >> the gaps left behind by the Reals. > > An answer! Just in case you are in an answering mood I'll try another: > > 0[1] is the first PO-point (and not a real) after 0. There are no real > points (I'll just call them reals) between 0 and 0[1]. The next point > on the number line (according to more than one post I've seen) is 0[2]. > Are there any reals between 0[1] and 0[2]? If so, how many? If not, > are there any between 0[2] and 0[3]? If so how many? If not, are there > any between 0[3] and 0[4]? Can you see where this is going? Can you > answer? By the way, it's fine to say you don't know. If you don't > know, please don't guess or bluff. > [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent points on a number line. There are no numbers of any kind what-so-ever Real or otherwise between any two immediately adjacent points on a number line. -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-20 02:34 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87o8zf4upg.fsf@bsb.me.uk> |
| In reply to | #211103 |
peteolcott <Here@Home> writes: > On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >> <cut> >>>>> As long as Integers can count ALL the points on a number line Cantor >>>>> is refuted. >>>> >>>> Not unless "a number line" includes the reals. >> <cut> >>> So although the number line does include every Real number it also >>> includes the more dense set of Infinitesimal numbers which fill in >>> the gaps left behind by the Reals. >> >> An answer! Just in case you are in an answering mood I'll try another: >> >> 0[1] is the first PO-point (and not a real) after 0. There are no real >> points (I'll just call them reals) between 0 and 0[1]. The next point >> on the number line (according to more than one post I've seen) is 0[2]. >> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >> are there any between 0[2] and 0[3]? If so how many? If not, are there >> any between 0[3] and 0[4]? Can you see where this is going? Can you >> answer? By the way, it's fine to say you don't know. If you don't >> know, please don't guess or bluff. > > [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent > points on a number line. > > There are no numbers of any kind what-so-ever Real or otherwise > between any two immediately adjacent points on a number line. So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? You are saying that 0[1], 0[2] and so on all come before any real number other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does not include any reals other than 0. You've said that "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 where are they? -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-19 20:54 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <8-WdnSEyGJrFrBnAnZ2dnUU7-VfNnZ2d@giganews.com> |
| In reply to | #211106 |
On 9/19/2019 8:34 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>> is refuted. >>>>> >>>>> Not unless "a number line" includes the reals. >>> <cut> >>>> So although the number line does include every Real number it also >>>> includes the more dense set of Infinitesimal numbers which fill in >>>> the gaps left behind by the Reals. >>> >>> An answer! Just in case you are in an answering mood I'll try another: >>> >>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>> points (I'll just call them reals) between 0 and 0[1]. The next point >>> on the number line (according to more than one post I've seen) is 0[2]. >>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>> answer? By the way, it's fine to say you don't know. If you don't >>> know, please don't guess or bluff. >> >> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >> points on a number line. >> >> There are no numbers of any kind what-so-ever Real or otherwise >> between any two immediately adjacent points on a number line. > > So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? > And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? > > You are saying that 0[1], 0[2] and so on all come before any real number > other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does > not include any reals other than 0. > > You've said that > > "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 where are they? > This last part must be incorrect because (for example) there are an infinite number of points between 0.0 and 0.1. There is also exactly the same number of points between 0.0 and ∞, so infinity is a somewhat incoherent concept. -- 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 | 2019-09-20 03:32 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87ef0b4s0j.fsf@bsb.me.uk> |
| In reply to | #211107 |
peteolcott <Here@Home> writes: > On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >>>> >>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>> peteolcott <Here@Home> writes: >>>> <cut> >>>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>>> is refuted. >>>>>> >>>>>> Not unless "a number line" includes the reals. >>>> <cut> >>>>> So although the number line does include every Real number it also >>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>> the gaps left behind by the Reals. >>>> >>>> An answer! Just in case you are in an answering mood I'll try another: >>>> >>>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>> on the number line (according to more than one post I've seen) is 0[2]. >>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>> answer? By the way, it's fine to say you don't know. If you don't >>>> know, please don't guess or bluff. >>> >>> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >>> points on a number line. >>> >>> There are no numbers of any kind what-so-ever Real or otherwise >>> between any two immediately adjacent points on a number line. >> >> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? >> >> You are saying that 0[1], 0[2] and so on all come before any real number >> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does >> not include any reals other than 0. >> >> You've said that >> >> "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 where are they? > > This last part must be incorrect What is "this last part"? Your statement "the number line does include every Real number" is indeed wrong, but that would be the end of the matter so I doubt you meant that. Where, in your counting, are the reals? Note that none of 0[1], 0[2], 0[3], ... can be a real number because which ever 0[k] it was would be the first real greater than 0 and you've (finally) agreed that there is no such real. And there are no reals /between/ any of the 0[k] either, so where are they in the counting? -- Ben.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-20 14:16 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qm2jfs$ttc$2@news.albasani.net> |
| In reply to | #211107 |
On 20/09/2019 02:54, peteolcott wrote: > On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >>>> >>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>> peteolcott <Here@Home> writes: >>>> <cut> >>>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>>> is refuted. >>>>>> >>>>>> Not unless "a number line" includes the reals. >>>> <cut> >>>>> So although the number line does include every Real number it also >>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>> the gaps left behind by the Reals. >>>> >>>> An answer! Just in case you are in an answering mood I'll try another: >>>> >>>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>> on the number line (according to more than one post I've seen) is 0[2]. >>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>> are there any between 0[2] and 0[3]? If so how many? If not, are >>>> there >>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>> answer? By the way, it's fine to say you don't know. If you don't >>>> know, please don't guess or bluff. >>> >>> [A[n], A[n+1]] (where n is an integer) specifies two immediately >>> adjacent >>> points on a number line. >>> >>> There are no numbers of any kind what-so-ever Real or otherwise >>> between any two immediately adjacent points on a number line. >> >> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? >> >> You are saying that 0[1], 0[2] and so on all come before any real number >> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does >> not include any reals other than 0. >> >> You've said that >> >> "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 where are they? >> > > This last part must be incorrect because (for example) there are an > infinite > number of points between 0.0 and 0.1. There is also exactly the same number > of points between 0.0 and ∞, so infinity is a somewhat incoherent concept. That's your concept of infinity. Mathematicians have coherent concepts of infinity. > >
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-20 17:49 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qm2vul$ak3$1@news.albasani.net> |
| In reply to | #211116 |
On 20/09/2019 14:16, Fred wrote: > On 20/09/2019 02:54, peteolcott wrote: >> On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> >>>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>>> peteolcott <Here@Home> writes: >>>>> <cut> >>>>>>>> As long as Integers can count ALL the points on a number line >>>>>>>> Cantor >>>>>>>> is refuted. >>>>>>> >>>>>>> Not unless "a number line" includes the reals. >>>>> <cut> >>>>>> So although the number line does include every Real number it also >>>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>>> the gaps left behind by the Reals. >>>>> >>>>> An answer! Just in case you are in an answering mood I'll try >>>>> another: >>>>> >>>>> 0[1] is the first PO-point (and not a real) after 0. There are no >>>>> real >>>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>>> on the number line (according to more than one post I've seen) is >>>>> 0[2]. >>>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>>> are there any between 0[2] and 0[3]? If so how many? If not, are >>>>> there >>>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>>> answer? By the way, it's fine to say you don't know. If you don't >>>>> know, please don't guess or bluff. >>>> >>>> [A[n], A[n+1]] (where n is an integer) specifies two immediately >>>> adjacent >>>> points on a number line. >>>> >>>> There are no numbers of any kind what-so-ever Real or otherwise >>>> between any two immediately adjacent points on a number line. >>> >>> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >>> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? >>> >>> You are saying that 0[1], 0[2] and so on all come before any real number >>> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does >>> not include any reals other than 0. >>> >>> You've said that >>> >>> "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 where are they? >>> >> >> This last part must be incorrect because (for example) there are an >> infinite >> number of points between 0.0 and 0.1. There is also exactly the same >> number >> of points between 0.0 and ∞, so infinity is a somewhat incoherent >> concept. > > That's your concept of infinity. Mathematicians have coherent concepts > of infinity. That it's concepts in the plural is relevant. Theories of infinitesimals also concern themselves with infinities. E.g., 1/(an infinitesimal) is an infinite number (different infinitesimals giving rise to different infinities). Also the theory of sets concerns itself infinities of two kinds: order types and cardinals (there are a plurality of order types with ordinals being a particular kind and the kind most often studied). If you muddle up these distinct kinds of infinity (and there are signs that you unthinkingly switch between 1/(infinitesimals), infinite ordinals and infinite cardinals. That the result is incoherent is hardly surprising. There are yet other infinities, e.g., Conway's surreal numbers have been mentioned. Will you look into these things (along with the real numbers) and work out just which is relevant? No. Will you think your ignorance is something to be proud of? Bizarrely, yes. I can seem some point in your pride. You lack the intellect to actually learn about the structure of the real numbers and instead of admitting to yourself that you lack the intellect you prefer to wear a badge of pride.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-20 07:16 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <IuadnRI8bKe4XhnAnZ2dnUU7-K_NnZ2d@giganews.com> |
| In reply to | #211106 |
On 9/19/2019 8:34 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>> <cut> >>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>> is refuted. >>>>> >>>>> Not unless "a number line" includes the reals. >>> <cut> >>>> So although the number line does include every Real number it also >>>> includes the more dense set of Infinitesimal numbers which fill in >>>> the gaps left behind by the Reals. >>> >>> An answer! Just in case you are in an answering mood I'll try another: >>> >>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>> points (I'll just call them reals) between 0 and 0[1]. The next point >>> on the number line (according to more than one post I've seen) is 0[2]. >>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>> answer? By the way, it's fine to say you don't know. If you don't >>> know, please don't guess or bluff. >> >> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >> points on a number line. >> >> There are no numbers of any kind what-so-ever Real or otherwise >> between any two immediately adjacent points on a number line. > > So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? > And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? > > You are saying that 0[1], 0[2] and so on all come before any real number > other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does > not include any reals other than 0. > > You've said that > > "0.0[1 to ∞] forms a bijection between the positive integers and all This last part must be incorrect because (for example) there are an infinite number of points between 0.0 and 0.1. > of the positive numbers through all of the positive points on the > number line" > > and "the number line does include every Real number" so where are they? > There is also exactly the same number of points between 0.0 and ∞, so infinity is a somewhat incoherent concept. -- 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 | 2019-09-20 21:37 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87woe23dqz.fsf@bsb.me.uk> |
| In reply to | #211114 |
peteolcott <Here@Home> writes: > On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: >> >>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>> peteolcott <Here@Home> writes: >>>> >>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>> peteolcott <Here@Home> writes: >>>> <cut> >>>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>>> is refuted. >>>>>> >>>>>> Not unless "a number line" includes the reals. >>>> <cut> >>>>> So although the number line does include every Real number it also >>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>> the gaps left behind by the Reals. >>>> >>>> An answer! Just in case you are in an answering mood I'll try another: >>>> >>>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>> on the number line (according to more than one post I've seen) is 0[2]. >>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>> answer? By the way, it's fine to say you don't know. If you don't >>>> know, please don't guess or bluff. >>> >>> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >>> points on a number line. >>> >>> There are no numbers of any kind what-so-ever Real or otherwise >>> between any two immediately adjacent points on a number line. >> >> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? Confirmation would allow progress. I'll assume you don't know. >> You are saying that 0[1], 0[2] and so on all come before any real number >> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does >> not include any reals other than 0. >> >> You've said that >> >> "0.0[1 to ∞] forms a bijection between the positive integers and all > > This last part must be incorrect because (for example) there are an infinite > number of points between 0.0 and 0.1. Please stop saying "that last part". What is it you are saying is wrong? Of all the wrong things you've said in these threads that "0.0[1 to ∞] forms a bijection between the positive integers" is one of the least wrong. Points of the form 0[k] with k in Z+, trivially biject with Z+. >> of the positive numbers through all of the positive points on the >> number line" >> >> and "the number line does include every Real number" so where are they? > > There is also exactly the same number > of points between 0.0 and ∞, so infinity is a somewhat incoherent > concept. You don't see the problem, do you? Your counting of the points does not hit even a single real, yet the reals are there in the "number line" and should be counted. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-20 15:53 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <8bGdnYaj3MSzoRjAnZ2dnUU7-KnNnZ2d@giganews.com> |
| In reply to | #211144 |
On 9/20/2019 3:37 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> >>>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>>> peteolcott <Here@Home> writes: >>>>> <cut> >>>>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>>>> is refuted. >>>>>>> >>>>>>> Not unless "a number line" includes the reals. >>>>> <cut> >>>>>> So although the number line does include every Real number it also >>>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>>> the gaps left behind by the Reals. >>>>> >>>>> An answer! Just in case you are in an answering mood I'll try another: >>>>> >>>>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>>> on the number line (according to more than one post I've seen) is 0[2]. >>>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>>> answer? By the way, it's fine to say you don't know. If you don't >>>>> know, please don't guess or bluff. >>>> >>>> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >>>> points on a number line. >>>> >>>> There are no numbers of any kind what-so-ever Real or otherwise >>>> between any two immediately adjacent points on a number line. >>> >>> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >>> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? > > Confirmation would allow progress. I'll assume you don't know. I answered this and you acknowledged that I answered this. > >>> You are saying that 0[1], 0[2] and so on all come before any real number >>> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does >>> not include any reals other than 0. >>> >>> You've said that >>> >>> "0.0[1 to ∞] forms a bijection between the positive integers and all >> >> This last part must be incorrect because (for example) there are an infinite >> number of points between 0.0 and 0.1. > > Please stop saying "that last part". What is it you are saying is THIS PART RIGHT HERE IS WRONG: 0.0[1 to ∞] > wrong? Of all the wrong things you've said in these threads that "e > least wrong. Points of the form 0[k] with k in Z+, trivially biject > with Z+. > >>> of the positive numbers through all of the positive points on the >>> number line" >>> >>> and "the number line does include every Real number" so where are they? >> >> There is also exactly the same number >> of points between 0.0 and ∞, so infinity is a somewhat incoherent >> concept. > > You don't see the problem, do you? Your counting of the points does not > hit even a single real, yet the reals are there in the "number line" and > should be counted. > This one: [0.0, ∞] hits ALL the numbers (including Reals) between 0.0 and ∞. This one: 0.0[1 to ∞] can't get past 0.1 -- 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 | 2019-09-21 00:10 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <87ftkq36os.fsf@bsb.me.uk> |
| In reply to | #211146 |
peteolcott <Here@Home> writes:
> On 9/20/2019 3:37 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/19/2019 8:34 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>
>>>>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote:
>>>>>>>> peteolcott <Here@Home> writes:
>>>>>> <cut>
>>>>>>>>> As long as Integers can count ALL the points on a number line Cantor
>>>>>>>>> is refuted.
>>>>>>>>
>>>>>>>> Not unless "a number line" includes the reals.
>>>>>> <cut>
>>>>>>> So although the number line does include every Real number it also
>>>>>>> includes the more dense set of Infinitesimal numbers which fill in
>>>>>>> the gaps left behind by the Reals.
>>>>>>
>>>>>> An answer! Just in case you are in an answering mood I'll try another:
>>>>>>
>>>>>> 0[1] is the first PO-point (and not a real) after 0. There are no real
>>>>>> points (I'll just call them reals) between 0 and 0[1]. The next point
>>>>>> on the number line (according to more than one post I've seen) is 0[2].
>>>>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not,
>>>>>> are there any between 0[2] and 0[3]? If so how many? If not, are there
>>>>>> any between 0[3] and 0[4]? Can you see where this is going? Can you
>>>>>> answer? By the way, it's fine to say you don't know. If you don't
>>>>>> know, please don't guess or bluff.
>>>>>
>>>>> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent
>>>>> points on a number line.
>>>>>
>>>>> There are no numbers of any kind what-so-ever Real or otherwise
>>>>> between any two immediately adjacent points on a number line.
>>>>
>>>> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes?
>>>> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes?
>>
>> Confirmation would allow progress. I'll assume you don't know.
>
> I answered this and you acknowledged that I answered this.
I'm still not sure. I'm going with yes. I'm sure you'll tell me if
that's not what you said before.
>>>> You are saying that 0[1], 0[2] and so on all come before any real number
>>>> other than 0. That means that the sequence 0[0], 0[1], 0[2], ... does
>>>> not include any reals other than 0.
>>>>
>>>> You've said that
>>>>
>>>> "0.0[1 to ∞] forms a bijection between the positive integers and all
>>>
>>> This last part must be incorrect because (for example) there are an infinite
>>> number of points between 0.0 and 0.1.
>>
>> Please stop saying "that last part". What is it you are saying is
>
> THIS PART RIGHT HERE IS WRONG: 0.0[1 to ∞]
Oh dear. That's the thing that "forms" the key to your whole claim.
You need to write the bijection you claim in some other way then.
>> wrong? Of all the wrong things you've said in these threads that "e
>> least wrong. Points of the form 0[k] with k in Z+, trivially biject
>> with Z+.
>>
>>>> of the positive numbers through all of the positive points on the
>>>> number line"
>>>>
>>>> and "the number line does include every Real number" so where are they?
>>>
>>> There is also exactly the same number
>>> of points between 0.0 and ∞, so infinity is a somewhat incoherent
>>> concept.
>>
>> You don't see the problem, do you? Your counting of the points does not
>> hit even a single real, yet the reals are there in the "number line" and
>> should be counted.
>
> This one: [0.0, ∞] hits ALL the numbers (including Reals) between 0.0
> and ∞.
You can't mean what those symbols mean. [0, oo] (or, to keep it in the
reals, [0, oo)) is just R+ U {oo}. It gives no hint about how to pick
the numbers off one by one. Pick off the first and you get (0, oo]
which is a set you've acknowledged has no first element (is order of
magnitude). You must be abusing conventional notation again (who'd have
thought you'd do that?).
And you can't mean all the reals with all your infinitesimals thrown in,
because for that set, you can count off an infinite list of
infinitesimals (0[0], 0[1], 0[2], ...) without hitting any reals other
than 0. What counting do you envisage for this thing you call [0, oo]
that enable you to count it?
> This one: 0.0[1 to ∞] can't get past 0.1
I am glad you can see that now. It can't get to even a single real
number. 0.1 is way to too far! Are there any other statements about
you PO-points that you need to retract?
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-21 09:45 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <euSdnZmm18kHqhvAnZ2dnUU7-KXNnZ2d@giganews.com> |
| In reply to | #211153 |
On 9/20/2019 6:10 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/20/2019 3:37 PM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: >>> >>>> On 9/19/2019 8:34 PM, Ben Bacarisse wrote: >>>>> peteolcott <Here@Home> writes: >>>>> >>>>>> On 9/19/2019 7:05 PM, Ben Bacarisse wrote: >>>>>>> peteolcott <Here@Home> writes: >>>>>>> >>>>>>>> On 9/19/2019 4:24 PM, Ben Bacarisse wrote: >>>>>>>>> peteolcott <Here@Home> writes: >>>>>>> <cut> >>>>>>>>>> As long as Integers can count ALL the points on a number line Cantor >>>>>>>>>> is refuted. >>>>>>>>> >>>>>>>>> Not unless "a number line" includes the reals. >>>>>>> <cut> >>>>>>>> So although the number line does include every Real number it also >>>>>>>> includes the more dense set of Infinitesimal numbers which fill in >>>>>>>> the gaps left behind by the Reals. >>>>>>> >>>>>>> An answer! Just in case you are in an answering mood I'll try another: >>>>>>> >>>>>>> 0[1] is the first PO-point (and not a real) after 0. There are no real >>>>>>> points (I'll just call them reals) between 0 and 0[1]. The next point >>>>>>> on the number line (according to more than one post I've seen) is 0[2]. >>>>>>> Are there any reals between 0[1] and 0[2]? If so, how many? If not, >>>>>>> are there any between 0[2] and 0[3]? If so how many? If not, are there >>>>>>> any between 0[3] and 0[4]? Can you see where this is going? Can you >>>>>>> answer? By the way, it's fine to say you don't know. If you don't >>>>>>> know, please don't guess or bluff. >>>>>> >>>>>> [A[n], A[n+1]] (where n is an integer) specifies two immediately adjacent >>>>>> points on a number line. >>>>>> >>>>>> There are no numbers of any kind what-so-ever Real or otherwise >>>>>> between any two immediately adjacent points on a number line. >>>>> >>>>> So no reals between 0[1] and 0[2]? And none between 0[2] and 0[3], yes? >>>>> And, indeed, none between 0[n] and 0[n+1] for every n in Z, yes? >>> >>> Confirmation would allow progress. I'll assume you don't know. >> >> I answered this and you acknowledged that I answered this. > > I'm still not sure. I'm going with yes. I'm sure you'll tell me if > that's not what you said before. > There are no reals in this sequence: 0.0[1 to ∞] (0.0, 1.0] is one point longer than (0.0, 1.0). Infinitesimals fill in the gaps between Reals, they have no bijection to Reals. 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. -- 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 | 2019-09-21 17:20 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <qm5ikp$ai9$1@news.albasani.net> |
| In reply to | #211155 |
On 21/09/2019 15:45, peteolcott wrote: > There are no reals in this sequence: 0.0[1 to ∞] > (0.0, 1.0] is one point longer than (0.0, 1.0). > Infinitesimals fill in the gaps between Reals, they have no bijection to > Reals. Are there fewer or more infinitesimals than real numbers? Or the same number? > 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. > >
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| From | Jim Burns <james.g.burns@att.net> |
|---|---|
| Date | 2019-09-21 14:39 -0400 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <78ddf8be-bb68-eb2d-2e72-f960f33697fa@att.net> |
| In reply to | #211155 |
On 9/21/2019 10:45 AM, peteolcott wrote:
> There are no reals in this sequence: 0.0[1 to ∞]
Cantor showed that there are _more_ real numbers
("number-line points") than natural numbers. Adding
_even more_ points, such as 0.0[1 to ∞] and similar,
will not give you _fewer_ points on the number line.
> (0.0, 1.0] is one point longer than (0.0, 1.0).
There is a bijection between (0.0, 1.0] and (0.0, 2.0].
For each point in (0.0,1.0], multiply it by 2, and
you get the corresponding point in (0.0, 2.0].
The (alleged) "last point" in (0.0, 2.0) should be
twice as far from 2.0 as the (alleged) "last point"
in (0.0, 1.0) is from 1.0, shouldn't it?
How does your theory account for this? Are the points
at or near 2.0 twice the size of the points at or
near 1.0?
Or do you have a different explanation?
> Infinitesimals fill in the gaps between Reals,
> they have no bijection to Reals.
The reals fill the gaps between reals. That's what makes
them the reals. The name for this is Dedekind completeness.
----
If you have a decreasing sequence of numbers 0.1, 0.01,
0.001, ... every number in it is positive, but, for any
fixed positive number x > 0, there are terms in the
decreasing sequence between x and 0.
Therefore, in order for a number x to be less than
_all_ the numbers in the sequence, x cannot be positive.
x can be 0 or x can be negative, but not positive.
Likewise, if you have an increasing sequence -0.1, -0.01,
-0.001, ... , in order for a number x to be greater than
_all_ the numbers in the increasing sequence, x can
be 0 or x can be positive, but not negative.
There is only one number which can be less than
every number in the higher, decreasing sequence and
also greater than every number in the lower, increasing
sequence: 0.
One could say, I suppose, that there is a one-point
_gap_ between the higher and lower sequences, right
where 0 is. The essential property of the reals is
that this gap is filled with a real number. And
(no surprise) that real number is 0.
This is boring, though. We already had 0 among the numbers
that we were using. If proving that 0 exists was our goal,
someone might wonder what the fuss is about.
The filling of these gaps becomes important when we
might not already have something at the gap among
the numbers we are using.
Suppose that the lower, increasing sequence is
3.1, 3.14, 3.141, 3.1415, 3.14159, 3.15192, ...
and the higher, decreasing sequence is
3.2, 3.15, 3.142, 3.1416, 3.14160, 3.15193, ...
What, if anything, is between the sequences?
If there were _no_ point between the sequences, there
would be a _gap_ . For example, if we were limited to
the rational numbers, we would still have our sequences
(since all the entries are rational), but we could not
have pi (which is not rational) between them. And no
other (rational) number could be there, either. And so,
we would have a gap in the rationals, one point "wide".
What makes the reals what they are is the declaration
that there _is_ a point between those sequences, and
also between all of the similar higher-decreasing and
lower-increasing sequences: "The reals have no gaps."
> A single point on the number line can be thought of
> as having a length somewhat comparable to 1.0/∞.
There doesn't appear to be any meaning that you
attach to this explanation.
> Everything that I said above supersedes and replaces
> everything else that I said.
When you find yourself superseding and replacing what
you've said before, then is a good time to see what
others have done and why they have done it.
Or not. Your call.
https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
----
Note that you, Pete Olcott, the kiddy-porn god, are STILL
objectively disgusting.
https://www.ketv.com/article/man-believed-child-porn-was-legal-because-he-was-god-authorities-say/7652218
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-22 13:32 +0100 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <874l143418.fsf@bsb.me.uk> |
| In reply to | #211155 |
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. > 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! -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-23 19:50 -0500 |
| Subject | Re: Provably unprovable eliminates incompleteness (CONCISE RESTATEMENT) |
| Message-ID | <sqidnS2gXpju9RTAnZ2dnUU7-IHNnZ2d@giganews.com> |
| In reply to | #211180 |
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. That no one else agrees is of no consequence. Prior to Pythagoras there was a universal consensus that the Earth was flat, thus proving that a consensus actually carries zero logical weight. >> 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! > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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