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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 2026-05-01 15:14 +0200
Organization tha
Message-ID <10t2907$17nch$1@solani.org> (permalink)
References (26 earlier) <10sscpf$3o7dr$1@dont-email.me> <10ssvgi$3ttpt$1@dont-email.me> <10sv5bq$hoit$1@dont-email.me> <10svj4f$m0qf$1@dont-email.me> <10t1ogn$19jlp$1@dont-email.me>

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Am 01.05.2026 um 10:33 schrieb Mikko:
> On 30/04/2026 15:49, WM wrote:
>> Am 30.04.2026 um 10:54 schrieb Mikko:
>>> On 29/04/2026 16:02, WM wrote:
>>>> Am 29.04.2026 um 09:42 schrieb Mikko:
>>>>> On 28/04/2026 16:18, WM wrote:
>>>>>> To cover every node of RRR... by paths going left after some node 
>>>>>> is as possible as to add even numbers with an odd result.
>>>>
>>>>> There are infinitely many paths to every node of RRR.
>>>>
>>>> No. That is provable only for nodes which have more successors than 
>>>> predecessors.
>>>
>>> It is true about the root node. All other nodes in the tree have a
>>> predecessor per the dfinition of "tree". All nodes have two successors
>>> (in this particular tree).
>>
>> All nodes that you can find or choose have more successors (namely 
>> infinitely many) than predecessors (namely finitely many).
> 
> If your "successor" includes successors of the successors and your
> "predecessor" includes predecessors of the predecessors then yes.

Of course they all are included.

> But it is true about all nodes.

That is not possible if "all" is a meaningful expression here. If all 
nodes are mapped, then none remains. That is not possible if only those 
nodes are mapped which have successors (because the successors remain).

>> Therefore it cannot be covered by other paths, not even by infinitely 
>> many.
> 
> No path can be covered by another path.

Yes. Nevertheless it is often claimed that a path like RRR... can be 
covered by an infinite sequence of other paths ending with LLL.... Since 
all paths of this sequence are useless, the claim is wrong, of course.>
>>>> My proof is simple: Every node except the root node separates only 
>>>> one more path.
>>>
>>> It does not. Infinitely many of the paths to the root continue to
>>> the left and infinitely many to the right. No more separation is
>>> introduced by that node. Nodes further down separate further but
>>> only to infinite subsets.
>>
>> So you deny the existence of single paths in the Binary Tree?
> 
> What does "single" mean above?

It means a sheave or separated subset containing only one path.>
> I do deny existence of nodes that don't have more than one path through
> them.
> 
Then you deny single paths. Then you deny Cantor's diagonal number as an 
isolated or separated single path. Theb you deny that 1/pi can be 
expressed by nodes oder digits. Of course it cannot be expressed, but 
you deny that it has an expression. Nevertheless a nice result of our 
discussion.

Regards, WM

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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 Mikko <mikko.levanto@iki.fi> - 2026-05-13 12:59 +0300
                Re: AI understands where 99 % of mathematicians fail wm <wolfgang.mueckenheim@tha.de> - 2026-05-13 22:50 +0200
                Re: AI understands where 99 % of mathematicians fail Mikko <mikko.levanto@iki.fi> - 2026-05-14 11:54 +0300
                Re: AI understands where 99 % of mathematicians fail WM <wolfgang.mueckenheim@tha.de> - 2026-05-14 17:00 +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

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