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| From | wm <wolfgang.mueckenheim@tha.de> |
|---|---|
| Newsgroups | sci.logic |
| Subject | Re: AI understands where 99 % of mathematicians fail |
| Date | 2026-03-22 14:00 +0100 |
| Organization | tha |
| Message-ID | <10pop4h$brd4$1@solani.org> (permalink) |
| References | (3 earlier) <10br9et$h42u$1@solani.org> <10pjpqg$bme8$1@solani.org> <10plp6v$2b8na$1@dont-email.me> <10pm40j$2eo3v$1@dont-email.me> <10pobqv$35gld$1@dont-email.me> |
Am 22.03.2026 um 10:13 schrieb Mikko:
> On 21/03/2026 14:47, WM wrote:
>> Am 21.03.2026 um 10:42 schrieb Mikko:
>>> On 20/03/2026 17:41, wm wrote:
>>>> “In the construction where exactly one path is assigned to each node
>>>> of the binary tree, every node is covered by at least one path.
>>>> Since the set of nodes is countable, the set of chosen paths is also
>>>> countable. Every infinite sequence of nodes—i.e., every path in the
>>>> tree—passes through at least one of these chosen paths.
>>>> Consequently, there is no additional path outside this set, and the
>>>> binary tree is completely covered by countably many paths.”
>>>> – ChatGPT, March 18, 2026
>>>>
>>> The error is in the sentence "Since the set of nodes is countable, the
>>> set of chosen paths is also countable". The expession "the set of chosen
>>> paths" is undefined,
>>
>> For every node one path containing is chosen. The set of chosen paths
>> therefore contains all possible infinite 0-1 combinations.
>
> How do you prove that no infinite 0-1 combination is in a path not
> chosen for any node?
Assume any node that starts a sequence of nodes that deviates from the
paths chosen by me. Every such node belongs to a path chosen by me,
because to every node there is a path.
> And how do you choose a path?
Path n goes to node n. The further fate of the path is irrelevant for my
argument.
> Do you apply some rule or do you assume
> some axiom of choice?
No choice necessary. The set of nodes is countable:
0
1 2
3 4 5 6
....
Path n goes from the root to node n.
Regards, WM
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AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-20 16:41 +0100
Re: AI understands where 99 % of mathematicians fail Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-03-20 19:06 +0000
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-20 22:57 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-21 11:42 +0200
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-21 13:47 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-22 11:13 +0200
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-22 14:00 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-23 11:52 +0200
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-23 16:33 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-24 10:33 +0200
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-24 20:29 +0100
Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-03-24 21:44 +0000
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 19:31 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 19:32 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-24 20:07 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-25 14:04 -0700
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-04-04 20:54 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) wm <wolfgang.mueckenheim@tha.de> - 2026-03-25 18:17 +0100
Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Alan Mackenzie <acm@muc.de> - 2026-03-25 17:55 +0000
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-25 10:44 +0200
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-25 18:31 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-26 10:18 +0200
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-26 17:21 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-27 11:52 +0200
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-27 19:04 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-28 11:20 +0200
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-03-28 17:03 +0100
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-29 12:02 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-29 14:44 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-30 11:49 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-30 12:39 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-31 12:33 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-29 16:45 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-30 11:58 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-30 12:38 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-03-31 12:51 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-03-31 18:34 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-01 11:12 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-01 13:59 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-02 10:35 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-02 20:29 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-03 10:10 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-04 17:54 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-05 10:22 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-05 17:15 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-06 11:12 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-06 19:55 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-07 11:07 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-07 16:07 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-08 10:14 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-08 12:51 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-09 12:35 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-09 17:44 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-10 11:01 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-10 13:01 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-11 10:54 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-11 17:05 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-12 12:49 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-12 13:50 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-13 10:16 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-13 12:54 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-14 09:16 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-14 20:38 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-15 10:18 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-15 16:20 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-16 11:41 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-16 16:26 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-17 10:08 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-17 15:10 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-18 12:52 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-18 14:40 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-19 12:55 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-19 12:55 +0200
Re: AI understands where 99 % of mathematicians fail Jeff Barnett <jbb@notatt.com> - 2026-04-17 01:13 -0600
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-17 15:21 +0200
Re: AI understands where 99 % of mathematicians fail Carlo XYZ <carloxyz@invalid.invalid> - 2026-04-06 08:26 +0200
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-04 17:58 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-05 10:28 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-05 17:20 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-06 11:22 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-06 20:03 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-07 11:11 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-07 17:07 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-08 10:20 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-08 12:56 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-09 12:40 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-09 17:46 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-10 11:07 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-10 13:03 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-11 11:00 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-11 17:10 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-12 13:02 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-12 13:55 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-13 10:28 +0300
Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-13 12:59 +0200
Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-14 09:24 +0300
Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-14 20:45 +0200
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