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Re: AI understands where 99 % of mathematicians fail

From Mikko <mikko.levanto@iki.fi>
Newsgroups sci.logic
Subject Re: AI understands where 99 % of mathematicians fail
Date 2026-05-08 10:40 +0300
Organization A noiseless patient Spider
Message-ID <10tk41e$2n699$1@dont-email.me> (permalink)
References (26 earlier) <10td0rh$gl8a$1@dont-email.me> <10tetnt$11smv$1@dont-email.me> <10tfb56$15u1k$1@dont-email.me> <10thf75$1rhod$1@dont-email.me> <10thpta$9cuu$1@solani.org>

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On 07/05/2026 13:35, wm wrote:
> 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.

Because he did not. It does not even make sense to say "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.

Every integer can be named. Every rational number can be named with
two integers. Nothing else satisfies the definition of "rational
number".

>> 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.

In constructive mathematics what cannot be constructed (of "found") does
not exist.

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

It seems that you don't have coherent opinions abot the binary tree.
At least your presentation has been incorerent.

-- 
Mikko

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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 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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