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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 | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-14 22:20 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <qljlis$j8h$3@news.albasani.net> |
| In reply to | #210701 |
On 14/09/2019 22:06, peteolcott wrote: > On 9/14/2019 3:55 PM, Fred wrote: >> On 14/09/2019 21:45, peteolcott wrote: >> >> >>> The common wisdom that a geometric point has zero width is now >>> proven to be incorrect. More accurately a single geometric >>> point has infinitesimal width. >> >> The common wisdom, as you call it, is indeed wise. He who says that a >> single geometric point has infinitesimal width is only making a useful >> statement if it is accompanied by a theory of infinitesimals. >> Luckily, there are theories of infinitesimals (see here >> https://en.wikipedia.org/wiki/Infinitesimal#Number_systems_that_include_infinitesimals >> for starters). Is any of them yours? If not, where may a coherent >> account of yours be found? >> >> > > Who else has proved that cardinality is incorrect? Nam! You're in good company!
[toc] | [prev] | [next] | [standalone]
| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 00:54 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <87woeafn8g.fsf@bsb.me.uk> |
| In reply to | #210701 |
peteolcott <Here@Home> writes: > Who else has proved that cardinality is incorrect? This week, I think it's only you. It's been a quiet few days here. -- Ben.
[toc] | [prev] | [next] | [standalone]
| From | Exfalso Quodlibet <exflaso.quodlibet@gmail.com> |
|---|---|
| Date | 2019-09-14 14:07 -0700 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <5372e565-d64a-47b8-a814-c8a204d53564@googlegroups.com> |
| In reply to | #210697 |
On Saturday, September 14, 2019 at 4:46:00 PM UTC-4, peteolcott wrote:
> That is contradicted by the fact that the interval (0.0, 1.0]
> has exactly one more geometric point than the interval (0.0, 1.0).
That doesn't change their length, any more than removing the number 1 from the set of naturals changes cardinality. {1,2,3,..} has the exact same cardinality as {2,3,4,...}, because we can create a bijection between them (namely, the function f(x)=x+1 to map from N to N\{1}).
> The common wisdom that a geometric point has zero width is now
> proven to be incorrect. More accurately a single geometric
> point has infinitesimal width.
Let's go with this. You use 0[1] to identify the point infinitesimally above 0, so presumably, this is also what you identify as the width of a point.
If we line up two points in a row, that means their length is 0[1]+0[1], which I assume is the same as 0[2]. And in general, if there are n points in a row, their combined length is 0[n]. Thus, for any natural number n, we have n*0[1]=0[1].
Now, does this property generalize to the real numbers? For any given real number r, does r*0[1]=0[r]? In particular, consider r=0.5. You seem to believe that the infinitesimal distance 0[1] is an indivisible, quantal unit, so 0[0.5] seems to be undefined, and thus, so is 0[r] for any real number r that isn't a natural number.
So how are we interpret r*0[1] in your system? Is multiplication with arbitrary real numbers simply not possible, and you can only use natural numbers? If so, that's a pretty restricted system, and certainly isn't useful for describing real numbers.
But until you define your system rigorously, there's no way for us to know.
EFQ
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-14 21:14 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <qljhmn$qtl$1@news.albasani.net> |
| In reply to | #210688 |
On 14/09/2019 20:41, peteolcott wrote: > On 9/14/2019 2:30 PM, Fred wrote: >> On 14/09/2019 20:27, peteolcott wrote: >>> On 9/14/2019 1:33 PM, Fred wrote: >>>> On 14/09/2019 19:09, peteolcott wrote: >>>> >>>>> It took me a long time to cut-and-paste this because all of the >>>>> variables >>>>> and symbols were images rather than Unicode: >>>> >>>> Spend as much time reading and comprehending as you do cutting and >>>> pasting, and you might gain some understanding. It's still wrong so >>>> your time was wasted. >>>> >>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>> Interval and segment >>>>> The simplest sets of points on the line. An interval (open >>>>> interval) is a set of points on a line lying between two fixed >>>>> points A and B, where A and B themselves are considered not to >>>>> belong to the interval. A segment (closed interval) is >>>>> a set of points between two points A and B, where A and B are >>>>> included. The terms "interval" and "segment" are also >>>>> used for the corresponding sets of real numbers: an interval >>>>> consists of numbers satisfying a < x < b, while a >>>>> segment consists of those x for which a ≤ x ≤ b. An interval is >>>>> denoted by (a, b), or ], and a segment by [a, b]. >>>> >>>> "or ]" makes no sense. >>>> >>>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>>> >>>> >>>> >>> >>> The first one is exactly one geometric point shorter than the second >>> one. >> >> The length of each of them is b - a. The length of a single point is 0. >> > > If the length of a single geometric point was actually zero then > the length of every interval would also be zero because 0 * ∞ = 0, > therefore the length of a single point on a number line is NOT zero. > You have hit upon an interesting point (is that a first?). But I would not write 0 * ∞, I would write 'the sum of infinitely many zeroes'. (It's an improvement because sums of infinite series are defined in terms of finitary objects. So matters relating to ∞ are avoided.) Ben Bacarisse mentioned measure theory, and it is there that these matters are addressed. Hawkins, /Lebesgue's theory/, Chlesea, is a nice read, but I have long since realised that you'd rather hold forth in ignorance than learn. The leap from the discrete to the continuous (like that from the countable to the uncountable) is mysterious but cleverer folk than you and I have it all worked out. Have you studied any probability theory? If so, did you ever notice that the "infinitely many zeroes making non-zero" problem occurs there too? Pick a number in [0,1] "at random". The probability that it is some particular x (0<=x<=1) is zero. The probability that it is in [0,1] is 1. But [0,1] is a collection of infinitely many x's each picked with zero probability.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 16:01 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <of6dnTdRafaLyODAnZ2dnUU7-SfNnZ2d@giganews.com> |
| In reply to | #210694 |
On 9/14/2019 3:14 PM, Fred wrote: > On 14/09/2019 20:41, peteolcott wrote: >> On 9/14/2019 2:30 PM, Fred wrote: >>> On 14/09/2019 20:27, peteolcott wrote: >>>> On 9/14/2019 1:33 PM, Fred wrote: >>>>> On 14/09/2019 19:09, peteolcott wrote: >>>>> >>>>>> It took me a long time to cut-and-paste this because all of the variables >>>>>> and symbols were images rather than Unicode: >>>>> >>>>> Spend as much time reading and comprehending as you do cutting and pasting, and you might gain some understanding. It's still wrong so your time was wasted. >>>>> >>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>> Interval and segment >>>>>> The simplest sets of points on the line. An interval (open interval) is a set of points on a line lying between two fixed >>>>>> points A and B, where A and B themselves are considered not to belong to the interval. A segment (closed interval) is >>>>>> a set of points between two points A and B, where A and B are included. The terms "interval" and "segment" are also >>>>>> used for the corresponding sets of real numbers: an interval consists of numbers satisfying a < x < b, while a >>>>>> segment consists of those x for which a ≤ x ≤ b. An interval is denoted by (a, b), or ], and a segment by [a, b]. >>>>> >>>>> "or ]" makes no sense. >>>>> >>>>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>>>> >>>>> >>>>> >>>> >>>> The first one is exactly one geometric point shorter than the second one. >>> >>> The length of each of them is b - a. The length of a single point is 0. >>> >> >> If the length of a single geometric point was actually zero then >> the length of every interval would also be zero because 0 * ∞ = 0, >> therefore the length of a single point on a number line is NOT zero. >> > You have hit upon an interesting point (is that a first?). But I would not write 0 * ∞, I would write 'the sum of infinitely many zeroes'. (It's an improvement because sums of infinite series are defined in terms of finitary objects. So matters relating > to ∞ are avoided.) Ben Bacarisse mentioned measure theory, and it is there that these matters are addressed. Hawkins, /Lebesgue's theory/, Chlesea, is a nice read, but I have long since realised that you'd rather hold forth in ignorance than learn. The > leap from the discrete to the continuous (like that from the countable to the uncountable) is mysterious but cleverer folk than you and I have it all worked out. > > Have you studied any probability theory? If so, did you ever notice that the "infinitely many zeroes making non-zero" problem occurs there too? Pick a number in [0,1] "at random". The probability that it is some particular x (0<=x<=1) is zero. The > probability that it is in [0,1] is 1. But [0,1] is a collection of infinitely many x's each picked with zero probability. > It is known that creative genius spends far less time acquiring domain knowledge. If I were to spend my time learning what everyone else every thought about these things before beginning my philosophical inquiries I would use up ten lifetimes before I ever get started. A first-principles approach (as Elon Musk and many others call it) is much more effective. -- 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 | 2019-09-14 22:17 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <qljld1$j8h$1@news.albasani.net> |
| In reply to | #210699 |
On 14/09/2019 22:01, peteolcott wrote: > On 9/14/2019 3:14 PM, Fred wrote: >> On 14/09/2019 20:41, peteolcott wrote: >>> On 9/14/2019 2:30 PM, Fred wrote: >>>> On 14/09/2019 20:27, peteolcott wrote: >>>>> On 9/14/2019 1:33 PM, Fred wrote: >>>>>> On 14/09/2019 19:09, peteolcott wrote: >>>>>> >>>>>>> It took me a long time to cut-and-paste this because all of the >>>>>>> variables >>>>>>> and symbols were images rather than Unicode: >>>>>> >>>>>> Spend as much time reading and comprehending as you do cutting and >>>>>> pasting, and you might gain some understanding. It's still wrong >>>>>> so your time was wasted. >>>>>> >>>>>>> https://www.encyclopediaofmath.org/index.php/Interval_and_segment >>>>>>> Interval and segment >>>>>>> The simplest sets of points on the line. An interval (open >>>>>>> interval) is a set of points on a line lying between two fixed >>>>>>> points A and B, where A and B themselves are considered not to >>>>>>> belong to the interval. A segment (closed interval) is >>>>>>> a set of points between two points A and B, where A and B are >>>>>>> included. The terms "interval" and "segment" are also >>>>>>> used for the corresponding sets of real numbers: an interval >>>>>>> consists of numbers satisfying a < x < b, while a >>>>>>> segment consists of those x for which a ≤ x ≤ b. An interval is >>>>>>> denoted by (a, b), or ], and a segment by [a, b]. >>>>>> >>>>>> "or ]" makes no sense. >>>>>> >>>>>> Anyway, all of (a,b), (a,b], [a,b) and [a,b] are intervals. >>>>>> >>>>>> >>>>>> >>>>> >>>>> The first one is exactly one geometric point shorter than the >>>>> second one. >>>> >>>> The length of each of them is b - a. The length of a single point >>>> is 0. >>>> >>> >>> If the length of a single geometric point was actually zero then >>> the length of every interval would also be zero because 0 * ∞ = 0, >>> therefore the length of a single point on a number line is NOT zero. >>> >> You have hit upon an interesting point (is that a first?). But I >> would not write 0 * ∞, I would write 'the sum of infinitely many >> zeroes'. (It's an improvement because sums of infinite series are >> defined in terms of finitary objects. So matters relating to ∞ are >> avoided.) Ben Bacarisse mentioned measure theory, and it is there >> that these matters are addressed. Hawkins, /Lebesgue's theory/, >> Chlesea, is a nice read, but I have long since realised that you'd >> rather hold forth in ignorance than learn. The leap from the discrete >> to the continuous (like that from the countable to the uncountable) is >> mysterious but cleverer folk than you and I have it all worked out. >> >> Have you studied any probability theory? If so, did you ever notice >> that the "infinitely many zeroes making non-zero" problem occurs there >> too? Pick a number in [0,1] "at random". The probability that it is >> some particular x (0<=x<=1) is zero. The probability that it is in >> [0,1] is 1. But [0,1] is a collection of infinitely many x's each >> picked with zero probability. >> > > It is known that creative genius spends far less time acquiring domain I am happy to let the creative geniuses do whatever they do. Meanwhile I'm in discussion with with a silly, ignorant person: a person who is so silly that that he thinks his ignorance is a virtue, a person who is so ignorant he doesn't know how silly he is. > knowledge. > > If I were to spend my time learning what everyone else every thought > about these > things before beginning my philosophical inquiries I would use up ten > lifetimes > before I ever get started. > > A first-principles approach (as Elon Musk Does Elon Musk know about your fondness for little boys? > and many others call it) is much > more effective. >
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 00:47 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <8736gyh247.fsf@bsb.me.uk> |
| In reply to | #210677 |
peteolcott <Here@Home> writes: > On 9/14/2019 11:23 AM, Ben Bacarisse wrote: >> peteolcott <Here@Home> writes: <cut> >>> The first point in this interval: (0.0, 1.0] very obviously >>> comes immediately after the first point in this interval: [0.0, 1.0]. >> >> There is no first point in the interval (0, 1] and that does not change >> if you write (0.0, 1.0] or (0.000. 1.000] because they all mean the same >> thing. (There are a lot of things that are false that you think are >> obviously true.) >> > > I READ YOUR WORDS INCORRECTLY, SORRY !!! OK. > On 9/12/2019 8:00 PM, Ben Bacarisse wrote: >> No. The common notational convention used for intervals shows that >> adjacent points do not exist. While [0, 1] has a least member, (0, 1] >> does not. You can remove the first number in [0, 1] to get (0, 1] but >> you can't remove the first and second. > > If we have a sequence of points [0.0, 1.0] on a number line and we remove > the first point (0.0, 1.0] then it is obvious that this second sequence is > exactly one geometric point shorter than the first sequence. The usual measure on intervals makes [0, 1] and (0, 1] the same length so you need to say PO-shorter, and then define what you mean by that. But this is a side issue. > The difference in length is that we removed the 1.0 point from the first > sequence leaving only the point that it was immediately adjacent to. That there is a first point in [0, 1] is not in dispute. > If we try to remove the next geometric point from the beginning of > this sequence we cannot only because there are no notational > conventions to say this. Some famous philosopher said that language > limits thought. No, you were able to express the thought perfectly well. You talked about "the point immediately adjacent to" 0. That is perfectly clear, and denotes something that does not exist. You can't do impossible things just by inventing notions for them. There is no number adjacent to 0, even if you say it's called 0[1]. You /can/ invent a set of objects of the form r[k] (provided you are prepared to work harder at defining them you seem prepared to be), but no one will care about them unless you can show them to be interesting in some way (and that's /way/ more work than you are prepared to do). > Since we just proved that adjacent geometric points exist, then by > induction there is always a next adjacent geometric point on the > number line. You don't know what a proof is if you think you have proved anything. -- Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 19:24 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <wvSdnW-vtIUDGeDAnZ2dnUU7-bvNnZ2d@giganews.com> |
| In reply to | #210712 |
On 9/14/2019 6:47 PM, Ben Bacarisse wrote: > peteolcott <Here@Home> writes: > >> On 9/14/2019 11:23 AM, Ben Bacarisse wrote: >>> peteolcott <Here@Home> writes: > <cut> >>>> The first point in this interval: (0.0, 1.0] very obviously >>>> comes immediately after the first point in this interval: [0.0, 1.0]. >>> >>> There is no first point in the interval (0, 1] and that does not change >>> if you write (0.0, 1.0] or (0.000. 1.000] because they all mean the same >>> thing. (There are a lot of things that are false that you think are >>> obviously true.) >>> >> >> I READ YOUR WORDS INCORRECTLY, SORRY !!! > > OK. > >> On 9/12/2019 8:00 PM, Ben Bacarisse wrote: >>> No. The common notational convention used for intervals shows that >>> adjacent points do not exist. While [0, 1] has a least member, (0, 1] >>> does not. You can remove the first number in [0, 1] to get (0, 1] but >>> you can't remove the first and second. >> >> If we have a sequence of points [0.0, 1.0] on a number line and we remove >> the first point (0.0, 1.0] then it is obvious that this second sequence is >> exactly one geometric point shorter than the first sequence. > > The usual measure on intervals makes [0, 1] and (0, 1] the same length > so you need to say PO-shorter, and then define what you mean by that. > But this is a side issue. > That is defining X = X + 1. The first interval contains 1.0, the second interval does not contain 1.0. >> The difference in length is that we removed the 1.0 point from the first >> sequence leaving only the point that it was immediately adjacent to. > > That there is a first point in [0, 1] is not in dispute. > >> If we try to remove the next geometric point from the beginning of >> this sequence we cannot only because there are no notational >> conventions to say this. Some famous philosopher said that language >> limits thought. > > No, you were able to express the thought perfectly well. You talked > about "the point immediately adjacent to" 0. That is perfectly clear, > and denotes something that does not exist. > It is self evidently the first point of this interval: (0.0, 1.0) > You can't do impossible things just by inventing notions for them. The above interval DOES HAVE A FIRST POINT. This point is the point immediately after 0.0. We cannot say that it does not exist ONLY BECAUSE EXISTING NUMBER SYSTEMS CANNOT EXPRESS IT. > There is no number adjacent to 0, even if you say it's called 0[1]. We know that there are a contiguous set of points between (0.0, 1.0] If we remove the last one then one of them the sequence is infinitesimally less than 1.0 long. > > You /can/ invent a set of objects of the form r[k] (provided you are > prepared to work harder at defining them you seem prepared to be), but > no one will care about them unless you can show them to be interesting > in some way (and that's /way/ more work than you are prepared to do). > As it stands it refutes cardinality. >> Since we just proved that adjacent geometric points exist, then by >> induction there is always a next adjacent geometric point on the >> number line. > > You don't know what a proof is if you think you have proved anything. > -- Copyright 2019 Pete Olcott All rights reserved "Great spirits have always encountered violent opposition from mediocre minds." Albert Einstein
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-15 02:20 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <qlk3k7$kjm$1@news.albasani.net> |
| In reply to | #210714 |
On 15/09/2019 01:24, peteolcott wrote:
> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>> <cut>
>>>>> The first point in this interval: (0.0, 1.0] very obviously
>>>>> comes immediately after the first point in this interval: [0.0, 1.0].
>>>>
>>>> There is no first point in the interval (0, 1] and that does not change
>>>> if you write (0.0, 1.0] or (0.000. 1.000] because they all mean the
>>>> same
>>>> thing. (There are a lot of things that are false that you think are
>>>> obviously true.)
>>>>
>>>
>>> I READ YOUR WORDS INCORRECTLY, SORRY !!!
>>
>> OK.
>>
>>> On 9/12/2019 8:00 PM, Ben Bacarisse wrote:
>>>> No. The common notational convention used for intervals shows that
>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>> you can't remove the first and second.
>>>
>>> If we have a sequence of points [0.0, 1.0] on a number line and we
>>> remove
>>> the first point (0.0, 1.0] then it is obvious that this second
>>> sequence is
>>> exactly one geometric point shorter than the first sequence.
>>
>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>> so you need to say PO-shorter, and then define what you mean by that.
>> But this is a side issue.
>>
>
> That is defining X = X + 1.
> The first interval contains 1.0, the second interval does not contain 1.0.
There are two sets [0,1] =df {x:0<=x<=1} and (0,1] =df {x:0<x<=1}. It
is true that the first contains an element that the second doesn't.
[Though that element is 0 not 1.] But how do you justify the leap from
that fact to the sets (now thought of as intervals) differ in length?
>>> The difference in length is that we removed the 1.0 point from the first
>>> sequence leaving only the point that it was immediately adjacent to.
>>
>> That there is a first point in [0, 1] is not in dispute.
>>
>>> If we try to remove the next geometric point from the beginning of
>>> this sequence we cannot only because there are no notational
>>> conventions to say this. Some famous philosopher said that language
>>> limits thought.
>>
>> No, you were able to express the thought perfectly well. You talked
>> about "the point immediately adjacent to" 0. That is perfectly clear,
>> and denotes something that does not exist.
>>
>
> It is self evidently the first point of this interval: (0.0, 1.0)
But no so self evident that anyone other than you gets it. (0,1) has no
first point.
>> You can't do impossible things just by inventing notions for them.
> The above interval DOES HAVE A FIRST POINT.
> This point is the point immediately after 0.0.
There is no such thing.
> We cannot say that it does not exist ONLY BECAUSE EXISTING NUMBER
> SYSTEMS CANNOT EXPRESS IT.
Go away and come back when you've invented a number system that does
express it. All you have is notation: x[y]. But you have failed to
explain how arithmetic is done with x[y].
Look up "non-standard analysis in Mendelson if you ever want to learn
about these things.
>> There is no number adjacent to 0, even if you say it's called 0[1].
>
> We know that there are a contiguous set of points between (0.0, 1.0]
> If we remove the last one then one of them the sequence is
> infinitesimally less than 1.0 long.
>
>>
>> You /can/ invent a set of objects of the form r[k] (provided you are
>> prepared to work harder at defining them you seem prepared to be), but
>> no one will care about them unless you can show them to be interesting
>> in some way (and that's /way/ more work than you are prepared to do).
>>
>
> As it stands it refutes cardinality.
Cardinality is a feature of sets (roughly the number of elements in a
set. Only roughly because a whole new class of numbers has to be
invented to make it so) as such it is not susceptible to refutation.
>>> Since we just proved that adjacent geometric points exist, then by
No you didn't because there's no such thing.
>>> induction there is always a next adjacent geometric point on the
>>> number line.
>>
>> You don't know what a proof is if you think you have proved anything.
>>
>
>
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 02:43 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY |
| Message-ID | <87ftkyfi60.fsf@bsb.me.uk> |
| In reply to | #210714 |
peteolcott <Here@Home> writes:
> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>> No. The common notational convention used for intervals shows that
>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>> you can't remove the first and second.
>>>
>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>> exactly one geometric point shorter than the first sequence.
>>
>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>> so you need to say PO-shorter, and then define what you mean by that.
>> But this is a side issue.
>
> That is defining X = X + 1.
No it isn't. It is defining length(X) = length(X U {0}) and this is
indeed the usual definition when both X and X U {0} are intervals.
Making an open interval closed does no change the length.
> The first interval contains 1.0, the second interval does not contain
> 1.0.
(Not important, but it's 0 not 1 that you removed in your example. I've
tried to stick with that.)
>>> The difference in length is that we removed the 1.0 point from the first
>>> sequence leaving only the point that it was immediately adjacent to.
>>
>> That there is a first point in [0, 1] is not in dispute.
>>
>>> If we try to remove the next geometric point from the beginning of
>>> this sequence we cannot only because there are no notational
>>> conventions to say this. Some famous philosopher said that language
>>> limits thought.
>>
>> No, you were able to express the thought perfectly well. You talked
>> about "the point immediately adjacent to" 0. That is perfectly clear,
>> and denotes something that does not exist.
>
> It is self evidently the first point of this interval: (0.0, 1.0)
Stating things does not make them true. The interval (0, 1) has no
first point. You can say that it "self evidently" does, in ALL CAPS,
repeated two dozen times, but it will still be false.
>> You can't do impossible things just by inventing notions for them.
> The above interval DOES HAVE A FIRST POINT.
There is no proof by ALL CAPS.
> This point is the point immediately after 0.0.
No, it still does not exist, even if you give it another name.
> We cannot say that it does not exist ONLY BECAUSE EXISTING NUMBER
> SYSTEMS CANNOT EXPRESS IT.
No, you can prove it does not exist. It is, actually, easy to express
in existing number systems, and the properties of the number system (R
in this case) rule (0, 1) having a first point.
>> There is no number adjacent to 0, even if you say it's called 0[1].
>
> We know that there are a contiguous set of points between (0.0, 1.0]
(Mathematicians would simply say that (0, 1] is contiguous. They would
never use "between (0, 1]" but they might very well say "in (0, 1]".)
> If we remove the last one then one of them the sequence is
> infinitesimally less than 1.0 long.
And you'd get (0, 1) which has no first not last number and has length 1.
>> You /can/ invent a set of objects of the form r[k] (provided you are
>> prepared to work harder at defining them you seem prepared to be), but
>> no one will care about them unless you can show them to be interesting
>> in some way (and that's /way/ more work than you are prepared to do).
>
> As it stands it refutes cardinality.
As it stands it's a vacuous claim. You haven't even clearly stated what
r can be. But please don't. If you want to know why you are wrong, go
back to the post where I asked follow-up questions and answer them.
There may even be more after that, but eventually you will state enough,
clearly enough, for me to be able to say if your PO-points fail to
include all the points, or if they include all the points and fail to be
a countable set.
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 21:33 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <c4OdneqApdJuP-DAnZ2dnUU7-YfNnZ2d@giganews.com> |
| In reply to | #210727 |
On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>> No. The common notational convention used for intervals shows that
>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>> you can't remove the first and second.
>>>>
>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>> exactly one geometric point shorter than the first sequence.
>>>
>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>> so you need to say PO-shorter, and then define what you mean by that.
>>> But this is a side issue.
>>
>> That is defining X = X + 1.
>
> No it isn't. It is defining length(X) = length(X U {0}) and this is
> indeed the usual definition when both X and X U {0} are intervals.
> Making an open interval closed does no change the length.
>
(0, 1] versus (0, 1) as a range of whole %
The first one is 0% to 100%
The second one is 0% to 99%
You can't magically ignore an actual difference just because it is infinitesimal.
(0, 1] a length of exactly 1.0
(0, 1) a length infinitesimally shorter than 1.0.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 04:09 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <87sgoydzm9.fsf@bsb.me.uk> |
| In reply to | #210732 |
peteolcott <Here@Home> writes:
> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>> No. The common notational convention used for intervals shows that
>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>> you can't remove the first and second.
>>>>>
>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>> exactly one geometric point shorter than the first sequence.
>>>>
>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>> But this is a side issue.
>>>
>>> That is defining X = X + 1.
>>
>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>> indeed the usual definition when both X and X U {0} are intervals.
>> Making an open interval closed does no change the length.
>
> (0, 1] versus (0, 1) as a range of whole %
> The first one is 0% to 100%
> The second one is 0% to 99%
No, that would be (0, 0.99) (or [0, 0.99]).
> You can't magically ignore an actual difference just because it is infinitesimal.
> (0, 1] a length of exactly 1.0
> (0, 1) a length infinitesimally shorter than 1.0.
It's not magic. Length is defined that way for a reason. As I have
said time and time again, just call your notion PO-length, define it
properly, and we can decide if we care about it or not.
--
Ben.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-14 22:40 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <T6idnb9L9ZxeL-DAnZ2dnUU7-XHNnZ2d@giganews.com> |
| In reply to | #210735 |
On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>> you can't remove the first and second.
>>>>>>
>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>
>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>> But this is a side issue.
>>>>
>>>> That is defining X = X + 1.
>>>
>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>> indeed the usual definition when both X and X U {0} are intervals.
>>> Making an open interval closed does no change the length.
>>
>> (0, 1] versus (0, 1) as a range of whole %
>> The first one is 0% to 100%
>> The second one is 0% to 99%
>
> No, that would be (0, 0.99) (or [0, 0.99]).
There are too many ways to correctly say this.
(0, 100] integers is 0 to 100
(0, 100) integers is 0 to 99
>
>> You can't magically ignore an actual difference just because it is infinitesimal.
>> (0, 1] a length of exactly 1.0
>> (0, 1) a length infinitesimally shorter than 1.0.
>
> It's not magic. Length is defined that way for a reason. As I have
> said time and time again, just call your notion PO-length, define it
> properly, and we can decide if we care about it or not.
>
0.0 to 100.0 including the 100 is 0 to 100.0
0.0 to 100.0 not including the 100 is 0 to 99.999999999999999999999999999999999999999... on to infinity
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-14 22:40 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qlkfbo$4iq$1@dont-email.me> |
| In reply to | #210738 |
On 2019-09-14 9:40 p.m., peteolcott wrote:
> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>> adjacent points do not exist. While [0, 1] has a least member,
>>>>>>>> (0, 1]
>>>>>>>> does not. You can remove the first number in [0, 1] to get (0,
>>>>>>>> 1] but
>>>>>>>> you can't remove the first and second.
>>>>>>>
>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and
>>>>>>> we remove
>>>>>>> the first point (0.0, 1.0] then it is obvious that this second
>>>>>>> sequence is
>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>
>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same
>>>>>> length
>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>> But this is a side issue.
>>>>>
>>>>> That is defining X = X + 1.
>>>>
>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>> Making an open interval closed does no change the length.
>>>
>>> (0, 1] versus (0, 1) as a range of whole %
>>> The first one is 0% to 100%
>>> The second one is 0% to 99%
>>
>> No, that would be (0, 0.99) (or [0, 0.99]).
>
> There are too many ways to correctly say this.
> (0, 100] integers is 0 to 100
> (0, 100) integers is 0 to 99
>
>>
>>> You can't magically ignore an actual difference just because it is
>>> infinitesimal.
>>> (0, 1] a length of exactly 1.0
>>> (0, 1) a length infinitesimally shorter than 1.0.
>>
>> It's not magic. Length is defined that way for a reason. As I have
>> said time and time again, just call your notion PO-length, define it
>> properly, and we can decide if we care about it or not.
>>
>
> 0.0 to 100.0 including the 100 is 0 to 100.0
> 0.0 to 100.0 not including the 100 is 0 to
> 99.999999999999999999999999999999999999999... on to infinity
Which is equal to exactly 1. The misconception that these two numbers
are different is sufficiently commonplace that it gets its own wikipedia
page.
<https://en.wikipedia.org/wiki/0.999...>
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
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| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-15 12:05 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qll5sv$p8m$1@news.albasani.net> |
| In reply to | #210738 |
On 15/09/2019 04:40, peteolcott wrote: > There are too many ways to correctly say this. > (0, 100] integers is 0 to 100 The integers in the set (0, 100] are 1,2,...,100. > (0, 100) integers is 0 to 99 The integers in the set (0, 100) are 1,2,...,99. So not correct in either case.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2019-09-15 12:33 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <87blvlequ8.fsf@bsb.me.uk> |
| In reply to | #210738 |
peteolcott <Here@Home> writes:
> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>> you can't remove the first and second.
>>>>>>>
>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>
>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>> But this is a side issue.
>>>>>
>>>>> That is defining X = X + 1.
>>>>
>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>> Making an open interval closed does no change the length.
>>>
>>> (0, 1] versus (0, 1) as a range of whole %
>>> The first one is 0% to 100%
>>> The second one is 0% to 99%
>>
>> No, that would be (0, 0.99) (or [0, 0.99]).
>
> There are too many ways to correctly say this.
> (0, 100] integers is 0 to 100
> (0, 100) integers is 0 to 99
No. Sadly, almost everything you post introduces new errors. There are
no open intervals in the integers so using the () notation is silly.
You can, of course, give it a meaning (as you have tried to do here) but
even then you get it wrong. If the "open" end means the bound is
excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
Why switch to integers which have totally different properties?
>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>> (0, 1] a length of exactly 1.0
>>> (0, 1) a length infinitesimally shorter than 1.0.
>>
>> It's not magic. Length is defined that way for a reason. As I have
>> said time and time again, just call your notion PO-length, define it
>> properly, and we can decide if we care about it or not.
>>
>
> 0.0 to 100.0 including the 100 is 0 to 100.0
> 0.0 to 100.0 not including the 100 is 0 to
> 99.999999999999999999999999999999999999999... on to infinity
I propose Ben's law: Every sufficiently long mathematical crank thread
ends up "debating" whether 0.999... = 1 or not.
No. 99.999... = 100 and you stated that 100 is not included.
There is no notation for the largest real in the open interval (0, 100),
not because no one has come up with a notation for it (that's trivial,
but the words will do) but because there is no such number.
This fact follows trivially from the definition of an open set in a
metric space, or from the axioms of the reals, or from the first baby
steps in topology... Repeatedly referring to a provably non-existent
object is just silly.
--
Ben.
[toc] | [prev] | [next] | [standalone]
| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 10:17 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <4bmdnZCR0LAZOuLAnZ2dnUU7-RfNnZ2d@giganews.com> |
| In reply to | #210753 |
On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>> you can't remove the first and second.
>>>>>>>>
>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>
>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>> But this is a side issue.
>>>>>>
>>>>>> That is defining X = X + 1.
>>>>>
>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>> Making an open interval closed does no change the length.
>>>>
>>>> (0, 1] versus (0, 1) as a range of whole %
>>>> The first one is 0% to 100%
>>>> The second one is 0% to 99%
>>>
>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>
>> There are too many ways to correctly say this.
>> (0, 100] integers is 0 to 100
>> (0, 100) integers is 0 to 99
>
> No. Sadly, almost everything you post introduces new errors. There are
> no open intervals in the integers so using the () notation is silly.
>
> You can, of course, give it a meaning (as you have tried to do here) but
> even then you get it wrong. If the "open" end means the bound is
> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>
> Why switch to integers which have totally different properties?
>
>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>> (0, 1] a length of exactly 1.0
>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>
>>> It's not magic. Length is defined that way for a reason. As I have
>>> said time and time again, just call your notion PO-length, define it
>>> properly, and we can decide if we care about it or not.
>>>
>>
>> 0.0 to 100.0 including the 100 is 0 to 100.0
>> 0.0 to 100.0 not including the 100 is 0 to
>> 99.999999999999999999999999999999999999999... on to infinity
>
> I propose Ben's law: Every sufficiently long mathematical crank thread
> ends up "debating" whether 0.999... = 1 or not.
>
> No. 99.999... = 100 and you stated that 100 is not included.
>
> There is no notation for the largest real in the open interval (0, 100),
> not because no one has come up with a notation for it (that's trivial,
> but the words will do) but because there is no such number.
>
Do you realize that you just said that the number line is defined with gaps?
There is either a contiguous set of points between 0 and 100 or there are
gaps between 0 and 100, those are the only two choices.
> This fact follows trivially from the definition of an open set in a
> metric space, or from the axioms of the reals, or from the first baby
> steps in topology... Repeatedly referring to a provably non-existent
> object is just silly.
>
https://www.encyclopediaofmath.org/index.php/Interval_and_segment
An interval (open interval) is a set of points on a line lying between two fixed
points A and B, where A and B themselves are considered not to belong to the interval.
This means that there is a first point and there is a last point of every
open interval. (0, 100) the first point is 0.0[1] and the last point is 100.0[-1].
(0,3] specifies a length of that is exactly one geometric point less than this [0,3].
Interpreted as integers
(0,3] specifies {1,2,3}
[0,3] specifies {0,1,2,3} which is 1.0 longer
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2019-09-16 09:26 -0600 |
| Subject | Re: Cantor was wrong about cardinality --- APOLOGY clear yet? |
| Message-ID | <qlo9jg$i6d$1@dont-email.me> |
| In reply to | #210799 |
On 2019-09-16 9:17 a.m., peteolcott wrote:
> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>> peteolcott <Here@Home> writes:
>>>>>>
>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>> No. The common notational convention used for intervals shows
>>>>>>>>>> that
>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least
>>>>>>>>>> member, (0, 1]
>>>>>>>>>> does not. You can remove the first number in [0, 1] to get
>>>>>>>>>> (0, 1] but
>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>
>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and
>>>>>>>>> we remove
>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second
>>>>>>>>> sequence is
>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>
>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same
>>>>>>>> length
>>>>>>>> so you need to say PO-shorter, and then define what you mean by
>>>>>>>> that.
>>>>>>>> But this is a side issue.
>>>>>>>
>>>>>>> That is defining X = X + 1.
>>>>>>
>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>> Making an open interval closed does no change the length.
>>>>>
>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>> The first one is 0% to 100%
>>>>> The second one is 0% to 99%
>>>>
>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>
>>> There are too many ways to correctly say this.
>>> (0, 100] integers is 0 to 100
>>> (0, 100) integers is 0 to 99
>>
>> No. Sadly, almost everything you post introduces new errors. There are
>> no open intervals in the integers so using the () notation is silly.
>>
>> You can, of course, give it a meaning (as you have tried to do here) but
>> even then you get it wrong. If the "open" end means the bound is
>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>
>> Why switch to integers which have totally different properties?
>>
>>>>> You can't magically ignore an actual difference just because it is
>>>>> infinitesimal.
>>>>> (0, 1] a length of exactly 1.0
>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>
>>>> It's not magic. Length is defined that way for a reason. As I have
>>>> said time and time again, just call your notion PO-length, define it
>>>> properly, and we can decide if we care about it or not.
>>>>
>>>
>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>> 0.0 to 100.0 not including the 100 is 0 to
>>> 99.999999999999999999999999999999999999999... on to infinity
>>
>> I propose Ben's law: Every sufficiently long mathematical crank thread
>> ends up "debating" whether 0.999... = 1 or not.
>>
>> No. 99.999... = 100 and you stated that 100 is not included.
>>
>> There is no notation for the largest real in the open interval (0, 100),
>> not because no one has come up with a notation for it (that's trivial,
>> but the words will do) but because there is no such number.
>>
>
> Do you realize that you just said that the number line is defined with
> gaps?
> There is either a contiguous set of points between 0 and 100 or there are
> gaps between 0 and 100, those are the only two choices.
No. You are describing a number line with gaps. He is not. If there were
indeed some largest real in the interval (0,100) (let's call it L), then
what number lies between L and 100? According to you, none. But, it is
axiomatic that for the real numbers, for every x and every y if z < y
then there exists some z such that x < z < y. This proves (by reductio
ad absurdum) that there is no such number L.
André
--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.
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| From | peteolcott <Here@Home> |
|---|---|
| Date | 2019-09-16 10:36 -0500 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <P9Kdnd8KC4x1NuLAnZ2dnUU7-XfNnZ2d@giganews.com> |
| In reply to | #210802 |
On 9/16/2019 10:26 AM, André G. Isaak wrote:
> On 2019-09-16 9:17 a.m., peteolcott wrote:
>> On 9/15/2019 6:33 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>
>>>> On 9/14/2019 10:09 PM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>
>>>>>> On 9/14/2019 8:43 PM, Ben Bacarisse wrote:
>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>
>>>>>>>> On 9/14/2019 6:47 PM, Ben Bacarisse wrote:
>>>>>>>>> peteolcott <Here@Home> writes:
>>>>>>>>>> On 9/14/2019 11:23 AM, Ben Bacarisse wrote:
>>>>>>>>>>> No. The common notational convention used for intervals shows that
>>>>>>>>>>> adjacent points do not exist. While [0, 1] has a least member, (0, 1]
>>>>>>>>>>> does not. You can remove the first number in [0, 1] to get (0, 1] but
>>>>>>>>>>> you can't remove the first and second.
>>>>>>>>>>
>>>>>>>>>> If we have a sequence of points [0.0, 1.0] on a number line and we remove
>>>>>>>>>> the first point (0.0, 1.0] then it is obvious that this second sequence is
>>>>>>>>>> exactly one geometric point shorter than the first sequence.
>>>>>>>>>
>>>>>>>>> The usual measure on intervals makes [0, 1] and (0, 1] the same length
>>>>>>>>> so you need to say PO-shorter, and then define what you mean by that.
>>>>>>>>> But this is a side issue.
>>>>>>>>
>>>>>>>> That is defining X = X + 1.
>>>>>>>
>>>>>>> No it isn't. It is defining length(X) = length(X U {0}) and this is
>>>>>>> indeed the usual definition when both X and X U {0} are intervals.
>>>>>>> Making an open interval closed does no change the length.
>>>>>>
>>>>>> (0, 1] versus (0, 1) as a range of whole %
>>>>>> The first one is 0% to 100%
>>>>>> The second one is 0% to 99%
>>>>>
>>>>> No, that would be (0, 0.99) (or [0, 0.99]).
>>>>
>>>> There are too many ways to correctly say this.
>>>> (0, 100] integers is 0 to 100
>>>> (0, 100) integers is 0 to 99
>>>
>>> No. Sadly, almost everything you post introduces new errors. There are
>>> no open intervals in the integers so using the () notation is silly.
>>>
>>> You can, of course, give it a meaning (as you have tried to do here) but
>>> even then you get it wrong. If the "open" end means the bound is
>>> excluded, then (0, 100] is 1 to 100 and (0, 100) is 1 to 99.
>>>
>>> Why switch to integers which have totally different properties?
>>>
>>>>>> You can't magically ignore an actual difference just because it is infinitesimal.
>>>>>> (0, 1] a length of exactly 1.0
>>>>>> (0, 1) a length infinitesimally shorter than 1.0.
>>>>>
>>>>> It's not magic. Length is defined that way for a reason. As I have
>>>>> said time and time again, just call your notion PO-length, define it
>>>>> properly, and we can decide if we care about it or not.
>>>>>
>>>>
>>>> 0.0 to 100.0 including the 100 is 0 to 100.0
>>>> 0.0 to 100.0 not including the 100 is 0 to
>>>> 99.999999999999999999999999999999999999999... on to infinity
>>>
>>> I propose Ben's law: Every sufficiently long mathematical crank thread
>>> ends up "debating" whether 0.999... = 1 or not.
>>>
>>> No. 99.999... = 100 and you stated that 100 is not included.
>>>
>>> There is no notation for the largest real in the open interval (0, 100),
>>> not because no one has come up with a notation for it (that's trivial,
>>> but the words will do) but because there is no such number.
>>>
>>
>> Do you realize that you just said that the number line is defined with gaps?
>> There is either a contiguous set of points between 0 and 100 or there are
>> gaps between 0 and 100, those are the only two choices.
>
>
> No. You are describing a number line with gaps. He is not. If there were indeed some largest real in the interval (0,100) (let's call it L), then what number lies between L and 100? According to you, none. But, it is axiomatic that for the real numbers,
> for every x and every y if z < y then there exists some z such that x < z < y. This proves (by reductio ad absurdum) that there is no such number L.
>
> André
>
>
Since it is clear that (0,100) specifies every geometric point on the number
line between 0 and 100 except for 0 and 100 then it does specify the geometric
point immediately after 0 and the geometric point immediately before 100 with
no geometric points in-between.
If these geometric points are defined to be real numbers and real numbers
are defined to always be divisible by 2, then something about the way that
these things are defined is inherently inconsistent.
--
Copyright 2019 Pete Olcott All rights reserved
"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein
[toc] | [prev] | [next] | [standalone]
| From | Fred <Fred@nowhere.invalid> |
|---|---|
| Date | 2019-09-16 16:50 +0100 |
| Subject | Re: Cantor was wrong about cardinality --- Reals are defined inconsistently |
| Message-ID | <qlob0m$9mr$1@news.albasani.net> |
| In reply to | #210805 |
On 16/09/2019 16:36, peteolcott wrote: > Since it is clear that (0,100) specifies every geometric point on the > number line between 0 and 100 except for 0 and 100 then it does > specify the geometric point immediately after 0 Call it x, so 0 < x. But then 0 < x/2 < x. Why isn't x/2 the geometric point immediately after 0? Or x/4, x/8, ...? > and the geometric > point immediately before 100 with no geometric points in-between. > > If these geometric points are defined to be real numbers and real > numbers are defined to always be divisible by 2, then something about > the way that these things are defined is inherently inconsistent. If I thought you had the wits to follow them, I'd recommend some books which define the real numbers in terms of simpler things (the rational numbers). There is more than one way to do it, see /Numbers/ by Ebbinghaus, Ewing, Hermes, Hirzebruch, etc, etc. Another approach is to specify some axioms (those for the complete ordered field) and say that the reals are just the things that satisfy those axioms. (That the axioms are categorical can be taken on trust or proved.)
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