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Groups > sci.math > #602228 > unrolled thread
| Started by | Peter Peters <pp1585024@gmail.com> |
|---|---|
| First post | 2023-06-14 03:35 -0700 |
| Last post | 2023-07-05 07:48 -0700 |
| Articles | 20 on this page of 165 — 16 participants |
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The mathematical constraints of set theory Peter Peters <pp1585024@gmail.com> - 2023-06-14 03:35 -0700
Re: The mathematical constraints of set theory Guckie <alberstein@freenet.de> - 2023-06-14 16:36 +0300
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 07:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 08:20 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 16:30 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 11:45 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:13 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 18:07 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 06:24 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 05:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-15 17:36 +0100
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 13:51 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:19 +0100
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 04:44 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 10:39 -0700
Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-27 09:00 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:13 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 15:45 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-14 10:08 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:44 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 08:03 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 08:29 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-16 09:03 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-16 13:30 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 12:08 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-17 06:26 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-17 09:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 05:57 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-18 07:01 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:13 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 10:09 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-17 10:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-18 09:40 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 05:05 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:15 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:22 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:38 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:40 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:24 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 09:11 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 11:27 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 11:44 -0700
Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 12:07 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 12:12 -0700
Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-20 06:43 -0700
Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-20 06:53 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-19 16:47 +0100
Re: The mathematical constraints of set theory Dieter Heidorn <d.heidorn@t-online.de> - 2023-06-19 20:11 +0200
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 00:08 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:49 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:35 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:09 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:13 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 18:35 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 03:04 +0100
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:52 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:54 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 15:42 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-27 08:39 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 02:43 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 04:32 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 15:16 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 07:48 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 16:43 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:49 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-29 09:59 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-30 13:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-30 18:09 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:25 -0700
Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-30 18:53 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 16:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-01 10:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-01 14:06 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:52 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 09:48 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 10:39 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 13:45 -0700
Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 14:09 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-02 14:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 07:01 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-03 13:09 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-04 08:33 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-04 18:43 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 10:39 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 08:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 13:14 -0400
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-06 06:27 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-09 06:41 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-09 07:58 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:40 -0700
Re: The mathematical constraints of set theory Tom Bola <Tom@bolamail.etc> - 2023-07-01 20:23 +0200
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 11:44 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:43 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 08:42 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 06:52 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-07-01 11:56 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 20:21 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:46 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:11 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 08:20 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:18 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 07:12 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:45 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:38 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:39 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:04 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-19 09:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:44 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 13:31 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:37 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:03 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:05 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:53 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:50 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-21 07:37 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:13 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 20:34 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:59 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-21 11:58 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:19 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-22 12:30 -0400
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 10:38 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 20:18 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:06 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:17 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:24 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:16 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 09:50 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 14:00 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:28 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:50 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-18 02:13 +0100
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:19 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:26 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 07:09 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 15:38 +0100
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 12:32 -0700
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-20 14:05 -0700
Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-21 04:43 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:33 -0700
Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:56 +0100
Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-17 18:34 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-14 16:50 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-14 20:19 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 17:08 -0400
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:45 -0700
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-16 14:58 -0400
Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 18:56 -0400
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-19 08:37 -0700
Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 11:16 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 00:23 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:54 -0700
Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 09:36 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-06 05:29 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-09 08:09 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:42 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 04:14 -0700
Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 07:27 -0700
Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 07:57 -0700
Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 07:48 -0700
Page 3 of 9 — ← Prev page 1 2 [3] 4 5 6 7 8 9 Next page →
| From | Gus Gassmann <horand.gassmann@gmail.com> |
|---|---|
| Date | 2023-06-19 09:11 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <4fb7a15c-4b32-4f72-9b90-8ddddf8da586n@googlegroups.com> |
| In reply to | #602687 |
On Monday, 19 June 2023 at 12:24:27 UTC-3, Timothy Golden wrote:
> On Monday, June 19, 2023 at 9:40:44 AM UTC-4, Gus Gassmann wrote:
> > On Monday, 19 June 2023 at 10:23:03 UTC-3, WM wrote:
> > > Gus Gassmann schrieb am Montag, 19. Juni 2023 um 15:15:46 UTC+2:
> > >
> > > > No idea what this means. Let me just give you this example (due to Galileo):
> > > > 1, 2, 3, 4, 5, ...
> > > > 1, 4, 9, 16, 25, ...
> > > >
> > > > The first row are the natural numbers, the second row are their squares. It is clear that the second row omits some natural numbers (such as 2 and 3, 5, 6, 7, 8, etc.). So on the face of it, it seems that there should be more natural numbers than square.
> > > >
> > > > On the other hand, it should be equally clear that to every natural number corresponds its square, so there ought to be the *same* number of squares as there are natural numbers.
> > > >
> > > The latter is wrong
> > Please fuck off, asshole. You are too stupid.
> For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega,
I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-19 11:27 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <e2b5d25a-583a-4429-b328-13285cba3699n@googlegroups.com> |
| In reply to | #602694 |
On Monday, June 19, 2023 at 6:11:34 PM UTC+2, Gus Gassmann wrote:
> On Monday, 19 June 2023 at 12:24:27 UTC-3, Timothy Golden wrote:
> >
> > For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega
> >
> I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
Same with Timothy Golden, btw.
So where does something like
{1, 3, 5, ... 2, 4, 6, ...} "stop (by)"
(where I assume an order < such that 1 < 3 < 5 < ... < 2 < 4 < 6 < ...).
[toc] | [prev] | [next] | [standalone]
| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-19 11:44 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <ceadff24-863e-499d-acf0-fd08e2de43bdn@googlegroups.com> |
| In reply to | #602694 |
On Monday, June 19, 2023 at 12:11:34 PM UTC-4, Gus Gassmann wrote:
> On Monday, 19 June 2023 at 12:24:27 UTC-3, Timothy Golden wrote:
> > On Monday, June 19, 2023 at 9:40:44 AM UTC-4, Gus Gassmann wrote:
> > > On Monday, 19 June 2023 at 10:23:03 UTC-3, WM wrote:
> > > > Gus Gassmann schrieb am Montag, 19. Juni 2023 um 15:15:46 UTC+2:
> > > >
> > > > > No idea what this means. Let me just give you this example (due to Galileo):
> > > > > 1, 2, 3, 4, 5, ...
> > > > > 1, 4, 9, 16, 25, ...
> > > > >
> > > > > The first row are the natural numbers, the second row are their squares. It is clear that the second row omits some natural numbers (such as 2 and 3, 5, 6, 7, 8, etc.). So on the face of it, it seems that there should be more natural numbers than square.
> > > > >
> > > > > On the other hand, it should be equally clear that to every natural number corresponds its square, so there ought to be the *same* number of squares as there are natural numbers.
> > > > >
> > > > The latter is wrong
> > > Please fuck off, asshole. You are too stupid.
> > For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega,
> I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
Gus this is an extremely weak response. You've cut out the strong points and focused on an admittedly weak one. I put 'stop' in singular quotes for a reason: this is weak reasoning. It is loose; not strict. Are the natural numbers strictly 1,2,3,...? Than are you claiming to construct a new set of numbers in their squares? Shouldn't this be done explicitly?
I gave you a fresh version carefully notated with aleph at the conclusion: 1,2,3,...,A.
Perhaps you are not as strong as I thought.
You've essentially marginalized yourself here.
To stretch a little is a good thing. Stretching too far could be a bad thing. If I did so then please attack, but that is not at all what this is.
This is a usenet dodge. You loose by that moniker.
Beyond this we know that mathematics has historically suffered abuse of type safety as this is a new concept; a new paradigm that has arrived as a result of programming languages. Set theory claims for instance that R is a subset of C. And yet C as RxR suggests you could go at it several ways. Especially through associative algebra the next level is in RxC, and now you've definitely got two options. This is ambiguous. Taking the naturals as a subset of the reals... is to take a discrete entity and swap it for a continuous one; rather a large change in quality. The reals still have not taken their proper form as gray numbers, which might then allow for a better transition, but instead the real value and its perfection goes against the spirit of all physical representation. Just here we bump into infinite precision, and so it is possible to take this tangent as wrapping back into the earlier discussion. Beyond all of this the physical continuum poses a serious need for actual mathematical correspondence, and that will be the gray value. Uncertainty is part of the deal. Close enough has to be good enough. No discrete matrix solution makes sense. Rotational freedom is enough to dissuade that attempt. From a cosmological scale it seems we don't need the infinite value; not when the universe has a size; albeit a growing size.
I accept a choice to reject all usage of infinity as a class of mathematics that has great practical value.
Stepping over that line... and to me it is the first usage of an ellipsis without an endpoint that steps over that line...
That is where the infinite begins. 1,2,3,...
If you'd like it is possible to claim that the discrete infinite breeds the continuum, but it will only resolve by confusing the aleph mark with the decimal point. This is a radix concept.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-19 12:07 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <5403f769-81f7-4918-8378-e03963b9d71an@googlegroups.com> |
| In reply to | #602714 |
On Monday, June 19, 2023 at 8:44:42 PM UTC+2, Timothy Golden wrote:
> I put 'stop' in singular quotes for a reason: this is weak reasoning. It is loose; not strict.
Indeed. It's nonsense.
> [...] are you claiming to construct a new set of numbers in their squares? Shouldn't this be done explicitly?
If you prefer. S := {n^2 : n e IN}. Not that hard, is it?
> I gave you a fresh version carefully notated with [some --FF] aleph at the conclusion: 1,2,3,...,A.
So what? This set is just IN u {A}. Then we may extend the usual order on the naturals such that An e IN: n < A holds (if A !e IN).
> Beyond this we know that mathematics has historically suffered abuse of type safety
Oh, really?! Didn't know that. Did Category Theory agree?
> I accept a choice to reject all usage of infinity as a class of mathematics that has great practical value.
See: https://en.wikipedia.org/wiki/Finitism
Or even: https://en.wikipedia.org/wiki/Ultrafinitism
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| From | Gus Gassmann <horand.gassmann@gmail.com> |
|---|---|
| Date | 2023-06-19 12:12 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <f6e4035d-208e-4ed1-be4a-1366c9a5aaf9n@googlegroups.com> |
| In reply to | #602714 |
On Monday, 19 June 2023 at 15:44:42 UTC-3, Timothy Golden wrote:
[...]
> > > For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega,
> > I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
> Gus this is an extremely weak response.
I concentrated on the first spot where it was impossible to follow you. And you admitted yourself that your point was weak. Since ex falso you can derive anything you like, there was no point to continue. As to the strength of your follow-up, I have no opinion; I did not bother to read further.
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| From | Timothy Golden <timbandtech@gmail.com> |
|---|---|
| Date | 2023-06-20 06:43 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <e4be155d-4fee-4404-aef9-53beb3a57df0n@googlegroups.com> |
| In reply to | #602721 |
On Monday, June 19, 2023 at 3:12:29 PM UTC-4, Gus Gassmann wrote:
> On Monday, 19 June 2023 at 15:44:42 UTC-3, Timothy Golden wrote:
> [...]
> > > > For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega,
> > > I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
> > Gus this is an extremely weak response.
> I concentrated on the first spot where it was impossible to follow you. And you admitted yourself that your point was weak. Since ex falso you can derive anything you like, there was no point to continue. As to the strength of your follow-up, I have no opinion; I did not bother to read further.
You must be an American!
Don't forget your daily slice of American cheese.
Fake America Fake Again.
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| From | Gus Gassmann <horand.gassmann@gmail.com> |
|---|---|
| Date | 2023-06-20 06:53 -0700 |
| Subject | Re: The mathematical constraints of set theoryn |
| Message-ID | <c675466c-d32f-45ae-a9c4-e096707fadd2n@googlegroups.com> |
| In reply to | #602771 |
On Tuesday, 20 June 2023 at 10:43:19 UTC-3, Timothy Golden wrote:
> On Monday, June 19, 2023 at 3:12:29 PM UTC-4, Gus Gassmann wrote:
> > On Monday, 19 June 2023 at 15:44:42 UTC-3, Timothy Golden wrote:
> > [...]
> > > > > For the moment I do see WM's reasoning here. Given that both sequences have to 'stop' by omega,
> > > > I don't even know what that means, "stop by". Neither the set {1, 2, 3, ...} nor the set {1, 4, 9, ...} contains omega. And BTW, WM has not *ever*, nor will he, produce correct reasoning on anything to do with mathematics.
> > > Gus this is an extremely weak response.
> > I concentrated on the first spot where it was impossible to follow you. And you admitted yourself that your point was weak. Since ex falso you can derive anything you like, there was no point to continue. As to the strength of your follow-up, I have no opinion; I did not bother to read further.
> You must be an American!
> Don't forget your daily slice of American cheese.
> Fake America Fake Again.
Sling your insults all you want. It is obvious that you have nothing substantive to contribute.
EOD.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-19 16:47 +0100 |
| Message-ID | <87fs6nlahc.fsf@bsb.me.uk> |
| In reply to | #602660 |
WM <askasker48@gmail.com> writes: (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des Unendlichen" at Hochschule Augsburg.) > Gus Gassmann schrieb am Montag, 19. Juni 2023 um 15:15:46 UTC+2: > >> No idea what this means. Let me just give you this example (due to Galileo): >> 1, 2, 3, 4, 5, ... >> 1, 4, 9, 16, 25, ... >> >> The first row are the natural numbers, the second row are their squares. It is clear that the second row omits some natural numbers (such as 2 and 3, 5, 6, 7, 8, etc.). So on the face of it, it seems that there should be more natural numbers than square. >> >> On the other hand, it should be equally clear that to every natural number corresponds its square, so there ought to be the *same* number of squares as there are natural numbers. >> > The latter is wrong as we can see easiest by the indexing of fractions: > > All positive fractions > > 1/1, 1/2, 1/3, 1/4, ... > 2/1, 2/2, 2/3, 2/4, ... > 3/1, 3/2, 3/3, 3/4, ... > 4/1, 4/2, 4/3, 4/4, ... > ... > > can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m Why don't you write it as a function? > which attaches the index k to the fraction m/n in Cantor's sequence This is a one-to-one correspondence between the fractions and the naturals which is what Gus was saying. You know that k(m,n) associates a unique index with every pair, and that k^-1 associates a unique pair with every index. It's very odd to say "that latter is wrong" and go on to give the formula that proves that "the latter" is correct. -- Ben.
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| From | Dieter Heidorn <d.heidorn@t-online.de> |
|---|---|
| Date | 2023-06-19 20:11 +0200 |
| Message-ID | <kfbk01Fh6hoU1@mid.individual.net> |
| In reply to | #602692 |
Ben Bacarisse schrieb:
> WM <askasker48@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> >> All positive fractions
>>
>> 1/1, 1/2, 1/3, 1/4, ...
>> 2/1, 2/2, 2/3, 2/4, ...
>> 3/1, 3/2, 3/3, 3/4, ...
>> 4/1, 4/2, 4/3, 4/4, ...
>> ...
>>
>> can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m
>
> Why don't you write it as a function?
>
If he would write
k: ℕxℕ --> ℕ ; k(m,n) = 1/2*(m + n - 2)*(m + n - 1) + n
it would be clear, that his proceeding - putting the k(m,n) in his
Matrix as elements M_(m,n) - is not the same as Cantors proceeding.
Further it would be clear, that his statement:
[WM] "Note that the only difference to Cantor's enumeration is that
_Cantor does not render account for the source of the indices_."
contains a lie. Cantor gave the "source of the indices":
|"Es hat nämlich die Funktion µ + ((µ + ny - 1)(µ + ny - 2))/2, wie
| leicht zu zeigen, die bemerkenswerte Eigenschaft, dass sie alle
| *positiven ganzen Zahlen* und jede nur einmal darstellt, wenn in ihr µ
| und ny unabhängig voneinander ebenfalls jeden positiven, ganzzahligen
| Wert erhalten."
https://gdz.sub.uni-goettingen.de/id/PPN243919689_0084?tify={%22pages%22%3A[261]%2C%22pan%22%3A{%22x%22%3A0.206%2C%22y%22%3A0.739}%2C%22view%22%3A%22export%22%2C%22zoom%22%3A0.528}
(translated:
|"Indeed, as can be easily shown, the function
| µ + ((µ + ny - 1) (µ + ny - 2))/2 has the remarkable property that it
| represents all *positive integers* and each one only once, if in it µ
| and ny independently also receive any positive integer value." )
> This is a one-to-one correspondence between the fractions and the
> naturals which is what Gus was saying.
There are a lot of people who share this statement... :-)
Dieter Heidorn
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-20 00:08 +0100 |
| Message-ID | <877crzjbj8.fsf@bsb.me.uk> |
| In reply to | #602711 |
Dieter Heidorn <d.heidorn@t-online.de> writes:
> Ben Bacarisse schrieb:
>> WM <askasker48@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Hochschule Augsburg.)
>> >> All positive fractions
>>>
>>> 1/1, 1/2, 1/3, 1/4, ...
>>> 2/1, 2/2, 2/3, 2/4, ...
>>> 3/1, 3/2, 3/3, 3/4, ...
>>> 4/1, 4/2, 4/3, 4/4, ...
>>> ...
>>>
>>> can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m
>> Why don't you write it as a function?
>>
>
> If he would write
>
> k: ℕxℕ --> ℕ ; k(m,n) = 1/2*(m + n - 2)*(m + n - 1) + n
>
> it would be clear, that his proceeding - putting the k(m,n) in his
> Matrix as elements M_(m,n) - is not the same as Cantors proceeding.
>
> Further it would be clear, that his statement:
>
> [WM] "Note that the only difference to Cantor's enumeration is that
> _Cantor does not render account for the source of the indices_."
>
> contains a lie. Cantor gave the "source of the indices":
I would be surprised if just writing it as a function would change his
mind.
> |"Es hat nämlich die Funktion µ + ((µ + ny - 1)(µ + ny - 2))/2, wie
> | leicht zu zeigen, die bemerkenswerte Eigenschaft, dass sie alle
> | *positiven ganzen Zahlen* und jede nur einmal darstellt, wenn in ihr µ
> | und ny unabhängig voneinander ebenfalls jeden positiven, ganzzahligen
> | Wert erhalten."
> https://gdz.sub.uni-goettingen.de/id/PPN243919689_0084?tify={%22pages%22%3A[261]%2C%22pan%22%3A{%22x%22%3A0.206%2C%22y%22%3A0.739}%2C%22view%22%3A%22export%22%2C%22zoom%22%3A0.528}
>
> (translated:
> |"Indeed, as can be easily shown, the function
> | µ + ((µ + ny - 1) (µ + ny - 2))/2 has the remarkable property that it
> | represents all *positive integers* and each one only once, if in it µ
> | and ny independently also receive any positive integer value." )
>
>
>> This is a one-to-one correspondence between the fractions and the
>> naturals which is what Gus was saying.
>
> There are a lot of people who share this statement... :-)
Yes, including WM! He has accepted that k(m,n) is bijective. I went on
to say
| You know that k(m,n) associates a unique index with every pair, and
| that k^-1 associates a unique pair with every index.
which was not just a rhetorical turn of phrase. He does indeed know
this.
--
Ben.
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-20 08:49 -0700 |
| Message-ID | <cd99c55c-0701-4218-bee7-d76d29934da7n@googlegroups.com> |
| In reply to | #602692 |
Ben Bacarisse schrieb am Montag, 19. Juni 2023 um 17:48:08 UTC+2: > WM <askas...@gmail.com> writes: > > All positive fractions > > > > 1/1, 1/2, 1/3, 1/4, ... > > 2/1, 2/2, 2/3, 2/4, ... > > 3/1, 3/2, 3/3, 3/4, ... > > 4/1, 4/2, 4/3, 4/4, ... > > ... > > > > can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m > Why don't you write it as a function? Why should I? > > which attaches the index k to the fraction m/n in Cantor's sequence > This is a one-to-one correspondence between the fractions and the > naturals which is what Gus was saying. You know that k(m,n) associates > a unique index with every pair, and that k^-1 associates a unique pair > with every index. It's very odd to say "that latter is wrong" and go on > to give the formula that proves that "the latter" is correct. It is not correct, since all O's remain in the matrix. It appears correct for all visible places of the matrix. Regards, WM
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-23 02:35 +0100 |
| Message-ID | <87h6qz7yfb.fsf@bsb.me.uk> |
| In reply to | #602784 |
WM <askasker48@gmail.com> writes:
> Ben Bacarisse schrieb am Montag, 19. Juni 2023 um 17:48:08 UTC+2:
>> WM <askas...@gmail.com> writes:
>
>> > All positive fractions
>> >
>> > 1/1, 1/2, 1/3, 1/4, ...
>> > 2/1, 2/2, 2/3, 2/4, ...
>> > 3/1, 3/2, 3/3, 3/4, ...
>> > 4/1, 4/2, 4/3, 4/4, ...
>> > ...
>> >
>> > can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m
>> Why don't you write it as a function?
>
> Why should I?
Because it is one? And if you claim it isn't one, what game are you
playing by pretending that it isn't one?
>> > which attaches the index k to the fraction m/n in Cantor's sequence
>> This is a one-to-one correspondence between the fractions and the
>> naturals which is what Gus was saying. You know that k(m,n) associates
>> a unique index with every pair, and that k^-1 associates a unique pair
>> with every index. It's very odd to say "that latter is wrong" and go on
>> to give the formula that proves that "the latter" is correct.
>
> It is not correct,
Which bit is not correct
(A) This is a one-to-one correspondence between the fractions and the
naturals
(B) which is what Gus was saying.
(C) You know that k(m,n) associates a unique index with every pair,
(D) and that k^-1 associates a unique pair with every index.
My guess is you won't say because all of A to D are correct.
--
Ben.
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| From | WM <askasker48@gmail.com> |
|---|---|
| Date | 2023-06-23 10:09 -0700 |
| Message-ID | <950588a6-97cf-4c6f-8c0e-ffd5f1e49f62n@googlegroups.com> |
| In reply to | #602998 |
Ben Bacarisse schrieb am Freitag, 23. Juni 2023 um 03:36:02 UTC+2: > WM <askas...@gmail.com> writes: > > It is not correct, > Which bit is not correct > (A) This is a one-to-one correspondence between the fractions and the > naturals No. That is true only for visible numbers. Most fractions remain without index. > (C) You know that k(m,n) associates a unique index with every pair, No, the O remain without index. Finally not even one O more is indexed than in the beginning. Regards, WM
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-23 10:19 -0700 |
| Message-ID | <bc429a4c-058e-4477-8cd9-9526893e41edn@googlegroups.com> |
| In reply to | #603043 |
On Friday, June 23, 2023 at 7:09:52 PM UTC+2, WM wrote: > No. That is true only for visible numbers. Most <bla> Please define the notion /visible numbers/. Yeah, "[WM’s] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-26 01:13 +0100 |
| Message-ID | <875y7b5bcv.fsf@bsb.me.uk> |
| In reply to | #603043 |
WM <askasker48@gmail.com> writes: (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des Unendlichen" at Hochschule Augsburg.) > Ben Bacarisse schrieb am Freitag, 23. Juni 2023 um 03:36:02 UTC+2: >> WM <askas...@gmail.com> writes: > >> > It is not correct, >> Which bit is not correct >> (A) This is a one-to-one correspondence between the fractions and the >> naturals > > No. That is true only for visible numbers. Most fractions remain > without index. ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m ∀i ∃n,m such that k(n,m) = i are both trivially provable. There are no pairs of naturals without an index. >> (C) You know that k(m,n) associates a unique index with every pair, > > No, the O remain without index. ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m ∀i ∃n,m such that k(n,m) = i are trivially provable. You can't insist that there are some numbers in N about which inductive proofs don't apply because of how N is defined. You don't get to add anything to our N. This is ironic, since the definition in you book has exactly the flaw you think mathematics has. Your N is not minimal, so you are wrong to say that f(x) = x (f: N->N) is bijective because of all the purple numbers in N. -- Ben.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-25 18:35 -0700 |
| Message-ID | <62868b01-9fe4-4525-a8ea-029b4669393an@googlegroups.com> |
| In reply to | #603292 |
On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote: > WM <askas...@gmail.com> writes: > > > > Most fractions remain without index. > > > ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m > ∀i ∃n,m such that k(n,m) = i > > are both trivially provable. Yes, but that does not refute his claim. His idiotc claim is: Ei,j such that k(i,j) !e IN Yes, this is braindead, since k is **defined** as a function with domain IN x IN and image IN. > There are no pairs of naturals without an index. Indeed, but your two claims from above do not concern t h i s point. (They ensure injectivity and surjectivity of k: IN x IN --> IN.) WM claims that k is a function such that there are some i,j e IN such that there is no n e IN with k(i,j) = n - even though k is explicitely defined such that all pairs (i,j) are mapped to some element(s) in IN. Imho WM is insane.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-26 03:04 +0100 |
| Message-ID | <87cz1j3ron.fsf@bsb.me.uk> |
| In reply to | #603296 |
Fritz Feldhase <franz.fritschee.ff@gmail.com> writes: > On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote: >> WM <askas...@gmail.com> writes: >> > >> > Most fractions remain without index. >> > >> ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m >> ∀i ∃n,m such that k(n,m) = i >> >> are both trivially provable. > > Yes, but that does not refute his claim. His idiotc claim is: > > Ei,j such that k(i,j) !e IN That's the translation of the claim into symbols, but I don't think that's what he means. He knows that k: NxN -> N as I am pretty sure that's been stated more than once, but he claims there are elements in N about which proofs are impossible. He will claim (I think) that Ei,j such that k(i,j) !e IN can't be proved either (otherwise we could ask for such a proof). > Yes, this is braindead, since k is **defined** as a function with > domain IN x IN and image IN. I don't think he will be prepared to deny this, but let's see. Maybe he will! -- Ben.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-25 19:52 -0700 |
| Message-ID | <25338733-5f38-4bdf-9c10-54bcf0cbfb95n@googlegroups.com> |
| In reply to | #603298 |
On Monday, June 26, 2023 at 4:04:18 AM UTC+2, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fri...@gmail.com> writes:
>
> > On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote:
> >> WM <askas...@gmail.com> writes:
> >> >
> >> > Most fractions are without index.
> >> >
> >> His idiotc claim [IN OTHER WORDS] is:
> > >
> > Ei,j such that k(i,j) !e IN
Actually, his claim is even stronger, since he does not just claim that there ARE such fractions, but MOST of them do not have an index.
> That's the translation of the claim into symbols,
Thank you very, I didn't notice that. (!)
> but I don't think that's what he means.
Oh really? So WHAT does "Most fractions are without index" mean in you book? Huh?!
Btw. we already had this discussion in de.sci.mathematik.
Hint: There he even denied that f(n) = n (f: IN --> IN) is a bijective function from IN onto IN. Reason: There are no bijections between infinite sets. ("They are not possible ") Period.
Hence k is not a bijection from IN x IN --> IN, no matter what you say.
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| From | Fritz Feldhase <franz.fritschee.ff@gmail.com> |
|---|---|
| Date | 2023-06-25 19:54 -0700 |
| Message-ID | <8a219cc1-df47-45bb-a4a0-ab5f08c6b5ebn@googlegroups.com> |
| In reply to | #603298 |
On Monday, June 26, 2023 at 4:04:18 AM UTC+2, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fri...@gmail.com> writes:
>
> > On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote:
> >> WM <askas...@gmail.com> writes:
> >> >
> >> > Most fractions remain without index.
> >> >
> >> ∀i,j,n,m k(n,m) = k(i,j) -> i=n and j=m
> >> ∀i ∃n,m such that k(n,m) = i
> >>
> >> are both trivially provable.
> >
> > Yes, but that does not refute his claim. His idiotc claim is:
> >
> > Ei,j such that k(i,j) !e IN
> That's the translation of the claim into symbols, but I don't think
> that's what he means. He knows that k: NxN -> N as I am pretty sure
> that's been stated more than once, but he claims there are elements in N
> about which proofs are impossible. He will claim (I think) that Ei,j
> such that k(i,j) !e IN can't be proved either (otherwise we could ask
> for such a proof).
> > Yes, this is braindead, since k is **defined** as a function with
> > domain IN x IN and image IN.
> I don't think he will be prepared to deny this, but let's see. Maybe he
> will!
On Monday, June 26, 2023 at 4:04:18 AM UTC+2, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fri...@gmail.com> writes:
>
> > On Monday, June 26, 2023 at 2:14:01 AM UTC+2, Ben Bacarisse wrote:
> >> WM <askas...@gmail.com> writes:
> >> >
> >> > Most fractions are without index.
> >> >
> >> His idiotc claim [IN OTHER WORDS] is:
> > >
> > Ei,j such that k(i,j) !e IN
Actually, his claim is even stronger, since he does not just claim that there ARE such fractions, but that MOST of them do not have an index.
> That's the translation of the claim into symbols,
Thank you very much, I didn't notice that. (!)
> but I don't think that's what he means.
Oh really? So WHAT does "Most fractions are without index" mean in you book? Huh?!
Btw. we already had this discussion in de.sci.mathematik.
Hint: There he even denied that f(n) = n (f: IN --> IN) is a bijective function from IN onto IN. Reason: There are no bijections between infinite sets. ("They are not possible ") Period.
Hence k is not a bijection from IN x IN --> IN, no matter what you say.
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2023-06-26 15:42 +0100 |
| Message-ID | <87jzvq2sl0.fsf@bsb.me.uk> |
| In reply to | #603304 |
Fritz Feldhase <franz.fritschee.ff@gmail.com> writes:
> On Monday, June 26, 2023 at 4:04:18 AM UTC+2, Ben Bacarisse wrote:
>> but I don't think that's what he means.
>
> Oh really? So WHAT does "Most fractions are without index" mean in you
> book? Huh?!
What matters is what he means, not what I mean! What he means will vary
from day to day and will sometimes depend on where in a circular
argument he currently stands.
I think today he is as the point where k is not a "finished" function
but a process where, at every step, only finitely many fractions have an
index and infinite many are without one. And in WM-land, that which is
true ate very step is just true. I would guess that the domain and
range are not in question today.
If and when this point of view becomes untenable, the dark numbers will
pop back and NxN will have "most" fraction dark about which inductive
proofs can say nothing. NxN will still have infinitely many unindexed
elements, but you won't be able to find any or even prove that there
exist (not that the don't) because... dark.
If he can be persuaded that N, and hence NxN, can have nothing in it
other than what we say, the process view will pop back.
> Btw. we already had this discussion in de.sci.mathematik.
>
> Hint: There he even denied that f(n) = n (f: IN --> IN) is a bijective
> function from IN onto IN. Reason: There are no bijections between
> infinite sets. ("They are not possible ") Period.
I've also already had this discussion (more than once). For example:
WM: k = (m + n - 1)(m + n - 2)/2 + m.
Me: I.e. k(n,m) is a bijection from NxN to N, a fact provable by any
student who has read your textbook. Do you agree that such a student
could prove this fact?
WM: Of course.
The textbook also includes examples. Specifically it states that f(x) =
x (where f is from N to N) is bijective.
> Hence k is not a bijection from IN x IN --> IN, no matter what you
> say.
That depends on what he means by a set and by a bjection today! k is
provably bijective or it does not exist. Take you pick.
--
Ben.
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