Groups | Search | Server Info | Login | Register

Groups > sci.logic > #345095

Re: AI understands where 99 % of mathematicians fail

From wm <wolfgang.mueckenheim@tha.de>
Newsgroups sci.logic
Subject Re: AI understands where 99 % of mathematicians fail
Date 2026-03-23 16:33 +0100
Organization tha
Message-ID <10prmgr$dqm9$1@solani.org> (permalink)
References (5 earlier) <10plp6v$2b8na$1@dont-email.me> <10pm40j$2eo3v$1@dont-email.me> <10pobqv$35gld$1@dont-email.me> <10pop4h$brd4$1@solani.org> <10pr2g7$1gvg$1@dont-email.me>

Show all headers | View raw

Am 23.03.2026 um 10:52 schrieb Mikko:
> On 22/03/2026 15:00, wm wrote:
>> 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.
> 
> There are infinitely may paths through every node. Therefore for every
> chosen path there are infinitely many other paths.

There is only one piece of path leading from the root to node n. This is 
covered by the paths chosen by me. This is true for all nodes. There are 
infinitely many paths but all are leading to nodes and therefore 
following my paths.
> 
>>> And how do you choose a path?
>>
>> Path n goes to node n. The further fate of the path is irrelevant for 
>> my argument.
> 
> It does matter whether the same path is chosen for some other node.

Only the piece from the root to node n is relevant. The further fate is 
irrelevant.
> 
>>> Do you apply some rule or do you assume
>>> some axiom of choice?
>>
>> No choice necessary. The set of nodes is countable:
> 
> Without choice you can't have any chosen paths. And the set of paths
> through a node is uncontable so the choice is not trivial.
> 
>>
>>     0
>>    1 2
>> 3 4 5 6
>> ....
>>
>> Path n goes from the root to node n.
> 
> As does infinitely many other paths.
> 
But each one of them passes nodes and therefore follows a path (indeed 
infinitely many) of my set. Note that all paths from level 0 to level n 
are covered by my set. This holds for all n ∈ ℕ. No paths going farther 
are available.

Regards, WM

Back to sci.logic | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

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 Mikko <mikko.levanto@iki.fi> - 2026-04-20 12:34 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-20 13:21 +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

csiph-web