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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	2026-03-29 14:44 +0200
Organization	tha
Message-ID	<10qb6s8$rqol$1@solani.org> (permalink)
References	(17 earlier) <10q5k0e$3kc8f$1@dont-email.me> <10q6gqu$3v305$1@dont-email.me> <10q86h2$fq5e$1@dont-email.me> <10q8u51$ojnr$1@dont-email.me> <10qaprb$1bp5e$1@dont-email.me>

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Am 29.03.2026 um 11:02 schrieb Mikko:
> On 28/03/2026 18:03, WM wrote:
>> Am 28.03.2026 um 10:20 schrieb Mikko:
>>> On 27/03/2026 20:04, WM wrote:
>>>> Am 27.03.2026 um 10:52 schrieb Mikko:
>>>>> On 26/03/2026 18:21, wm wrote:
>>>>>> Am 26.03.2026 um 09:18 schrieb Mikko:
>>>>>>> On 25/03/2026 19:31, WM wrote:
>>>>>>
>>>>>>>> Every node N(n) is mapped to a path P(n). (Maybe that two or 
>>>>>>>> more nodes are mapped to the same path, but that does not 
>>>>>>>> invalidate my proof.) There are countably many nodes, hence 
>>>>>>>> there are countably many paths.
>>>>>>>
>>>>>>> The last sentence is false. It should say that the all nodes are 
>>>>>>> mapped
>>>>>>> to a countable subset of all paths.
>>>>>>
>>>>>> Yes, there are countably many paths in the set P of paths that I 
>>>>>> apply. Try find a path that does not belong to this countable set P.
>>>>>
>>>>> You did not specify a particuar P.
>>>>
>>>> Every node is mapped to a path of P. These paths start with the root 
>>>> node and go to their node. The tail is what you like.
>>>
>>> I like to to be always to the left subnode.
>>
>> Fine. But that does not satisfy my criterion.
> 
> You did not specify any criterion for the rest of the path. Instead you
> said that I can choose whatever I want.

Yes, but you must comply with my criterion: Every knode is mapped to a 
path that contains it.
> 
>> If you consider the utmost right path RRR... , turning always right, 
>> then it is impossible to cover all its nodes unless the path itself 
>> belongs to the set P.
> 
> Every path in P contains only a finite number of right turns so the paht
> that contains only right turns is not P.

Then there is at least one node not mapped to a path in P, disobeying 
the basic condition.
Note that each one of your paths turn off before all nodes are covered.
If all nodes of a path are covered, then this path is in P.

> What is important about P other than that it does not contain all paths?

I all nodes of a path are covered, then this path belongs to P.
> 
>> If you consider the path LRRR... which first turns left and then 
>> always right, then it is impossible to cover all its nodes unless the 
>> path itself belongs to the set P. (Note that there is no other path 
>> which could help,)
> 
> That path is not in P because it contains infinitely many right turns.
> However, it covers all its nodes.

Covering all nodes means that there is a direct path from the root to 
infinity. Every deviating path is not this path and every set of 
deviating paths cannot cover it.

> In addition, althogh no path in P
> covers all its nodes,

Then not all its nodes are covered. It is impossible for a set of paths 
to cover more than the best path can cover.

> each node is covered by the path that node is
> mapped to, and that paht is in P.

Every deviating path fails to cover RRR... .

>> Your argument has been stated in the German Newgroup de.sci.mathematik 
>> in exactly the same form. When I informed the author he accused me of 
>> changing the conditions. Therefore I informed you immediately.
> 
> Your "But that does not satisfy my criterion" may be interpreted as a
> change of conditions.

It is not.

> But I interprete that the conditions cannot be
> changed and that you just presented a false statement.d, then the path is covered.

If all nodes of a path are dovered, then the path is in P. Only the path 
itself can cover all its nodes. Each one of your paths turn off and 
leave nodes uncoverd.
> 
>> But you can be sure that my set of paths covers the whole Binary Tree.
> 
> OK.
> 
Therefore no additional path is existing.

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 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 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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