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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Mon, 11 Nov 2024 13:17:52 +0200
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On 2024-11-10 10:56:26 +0000, WM said:

> On 10.11.2024 11:20, Mikko wrote:
>  > On 2024-11-09 21:30:47 +0000, WM said:
>  >
>  >> On 09.11.2024 15:03, Mikko wrote:
>  >>> On 2024-11-08 16:30:23 +0000, WM said:
>  >>
>  >>>>
>  >>>> If Cantors enumeration of the rationals is complete, then all rationals
>  >>>> are in the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 
> 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1,  ... and 
> none is outside.
>  >>>
>  >>> All positive rationals quite obviously are in the sequence. Non-positive
>  >>> rationals are not.
>  >>>
>  >>>> Therefore also irrational numbers cannot be there.
>  >>>
>  >>> That is equally obvious.
>  >>>
>  >>>> Of course this is wrong.
>  >>>
>  >>> You may call it wrong but that's the way they are.
>  >>
>  >> The measure of all intervals J(n) = [n - √2/10, n + √2/10] is 
> smaller than 3.
>  >
>  > Maybe, maybe not, depending on what is all n.
> 
> It is, as usual, all natural numbers.
> 
>  > If all n is all reals then
>  > the measure of their union is infinite.
> 
> But n is all naturals as you could have found out yourself, by the measure < 3.

That is not something one can find out. The symbol n means whatever you
say it means, and in this case you didn't say.

-- 
Mikko