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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 2026-05-07 12:35 +0200
Organization tha
Message-ID <10thpta$9cuu$1@solani.org> (permalink)
References (26 earlier) <10tcci8$abdm$1@dont-email.me> <10td0rh$gl8a$1@dont-email.me> <10tetnt$11smv$1@dont-email.me> <10tfb56$15u1k$1@dont-email.me> <10thf75$1rhod$1@dont-email.me>

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Am 07.05.2026 um 09:32 schrieb Mikko:
> On 06/05/2026 15:11, WM wrote:
>> Am 06.05.2026 um 10:22 schrieb Mikko:
>>> On 05/05/2026 18:03, WM wrote:
>>
>>>> There are dark numbers. When you choose a natural number, then it 
>>>> has more successors than predecessors. When you choose the 
>>>> collection "all natural" numbers then none remains.That proves that 
>>>> you cannot choose every natural number as an individual. Same is 
>>>> true for nodes.
>>>
>>> Whdn we need to choose an individual node or an individual natural
>>> number we don't care about all of them. When we need to say something 
>>> about every node or every natural number we con't care about individial
>>> ones.
>>
>> con't means can't? Then you said a truth. And in particular with reals 
>> we see the idea of dark numbers even better: Between two real numbers 
>> there are infinitely many real numbers, infinitely many of which you 
>> cannot name whatever you try.
> It is well known that there are uncaountably many reals between any two
> different reals but only cauntably many names. An obvious conseqence is
> that most of the reals have no name.

Nice that you understand this. But many do not. A preprint by J.D. 
Hamkins et al. contains the following phrases, starting smugly: "One 
occasionally hears the argument – let us call it the math-tea argument, 
for perhaps it is heard at a good math tea – that there must be real 
numbers that we cannot describe or define, because there are only 
countably many definitions, but uncountably many reals. Does it 
withstand scrutiny? [...]
	Question 1. Is it consistent with the axioms of set theory that every 
real is definable in the language of set theory without parameters?
	The answer is Yes. Indeed, much more is true: if the ZFC axioms of set 
theory are consistent, then there are models of ZFC in which every 
object, including every real number, every function on the reals, every 
set of reals, every topological space, every ordinal and so on, is 
uniquely definable without parameters. [J.D. Hamkins et al.: "Pointwise 
definable models of set theory", arXiv (2012)]

Obviously he has not understood that he disproved ZFC. But 
uncountability is not the reason for the existence of undefinable 
numbers because between two rational numbers on the real line there are 
infinitely many rational numbers, infinitely many of which you cannot 
name whatever you try.

> In constructive mathematics, where nothing unnamed exists, it is
> provable that reals are not constructively countable.

Even there we have most rational numbers between two given rational 
numbers can never be found although they must be there in actual infinity.

At least in the Binary Tree all should be present unless darkness veils 
them.

Regards, WM

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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 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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