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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 2026-04-20 13:21 +0200
Organization tha
Message-ID <10s527r$k7bq$1@solani.org> (permalink)
References (26 earlier) <10rvk8j$34bvb$2@dont-email.me> <10rvu3g$i05c$1@solani.org> <10s28qd$3slji$1@dont-email.me> <10s2cab$ie67$1@solani.org> <10s4rvo$kb81$1@dont-email.me>

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Am 20.04.2026 um 11:34 schrieb Mikko:
> On 19/04/2026 13:55, wm wrote:
>> Am 19.04.2026 um 11:55 schrieb Mikko:
>>> On 18/04/2026 15:40, wm wrote:
>>
>>>>> Does "complete" imply that every node has two subnodes?
>>>>
>>>> Of course. This allows a simple mapping: Every node splits a sheaf 
>>>> into two sheaves. The node is mapped to one of them. It does not 
>>>> matter to which one, because the other sheaf carries a node from a 
>>>> higher  level.
>>> That is sufficient for my proofs.
>>
>> Then we have found a contradiction-
> 
> Then the next step is to extract from that contracidtion a simpler
> contradiction, preferably the simplest possible one.

See below. I think there is the simplest possible contradiction.

> One may even
> hope that it could be simplified to something that can be published
> as a paradox.

It has been published already:
W. Mückenheim: "Transfinity - A Source Book", ELIVA Press, Chisinau 
(2024). p. 283
https://www.elivapress.com/en/book/book-9877032691/
The tunnel effect of set theory, reddit/mathematics (12 April 2026)
https://www.reddit.com/r/mathematics/comments/1sjdj57/the_tunnel_effect_of_set_theory/


> 
>>> If the tree is complete in that sense then it also is infinite and its
>>> every subtree is also complete in that sense and infinite.
>>
>> Here is the proof of equicardinality of nodes and paths:
>>
>>     |
>>     |
>>     |
>>     v
>>     O
>>    / \
>>   /   \
>> |     |
>> v     v
>>
>> And even clearer:
>>
>> |
>> |
>> |
>> |      O
>> |      |
>> |      |
>> v      v
> 
> No, neither is a proof of anything. For a proof of equicardinality
> you need to proofs of that every requirement in the definition of
> equicardinality is satisfied.

It is. Every node produces one and only one new sheaf. It is a bijection.

Regards, WM

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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: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Moebius <invalid@example.invalid> - 2026-04-30 04:43 +0200
            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> - 2026-04-30 09:10 -0700
              Re: Criticism of a proof of a contradiction in set theory (Was: Re: AI understands where 99 % of mathematicians fail) Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:55 +0300
                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> - 2026-05-01 09:47 -0700
              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> - 2026-05-01 15:20 +0200
        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 Mikko <mikko.levanto@iki.fi> - 2026-04-21 10:25 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-04-21 12:46 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:03 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-22 15:21 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:40 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-23 15:01 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:45 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-24 14:59 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-25 12:14 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-25 15:36 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-26 11:30 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-26 21:33 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-27 13:03 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-27 12:19 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:22 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-28 15:18 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:42 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-29 15:02 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-04-30 11:54 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-04-30 14:49 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:33 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-01 15:14 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:47 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-02 16:02 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-03 11:09 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-03 13:30 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-04 09:37 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-04 12:47 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-05 12:16 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-05 17:03 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-06 11:22 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-06 14:11 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-07 10:32 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-07 12:35 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-08 10:40 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-08 14:26 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-09 10:39 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-10 15:47 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-11 10:39 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-11 12:56 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-12 10:19 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-12 12:52 +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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