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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Mon, 11 Nov 2024 12:33:52 +0100
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On 11.11.2024 12:15, Mikko wrote:
> On 2024-11-10 10:54:02 +0000, WM said:
> 

>>>>
>>>> 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.
> 
> The measure of the interval J(n) is √2/5, which is roghly 0,28.

Agreed, I said smaller than 3.

> The measure of the set of all those intervals is infinite.

The density or relative measure is √2/5. By shifting intervals this 
density cannot grow. Therefore the intervals cannot cover the real axis, 
let alone infinitely often.

> Between the intervals J(n) and (Jn+1) there are infinitely many rational
> and irrational numbers but no hatural numbers.
> 
Therefore infinitely many natural numbers must become centres of 
intervals, if Cantor was right. But that is impossible.

Regards, WM