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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: Tue, 12 Nov 2024 15:45:53 +0200
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On 2024-11-11 11:33:52 +0000, WM said:

> 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.

Where did Cantor say otherwise?

-- 
Mikko