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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: Wed, 13 Nov 2024 12:39:39 +0200
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On 2024-11-12 13:59:24 +0000, WM said:

> On 12.11.2024 14:45, Mikko wrote:
>> On 2024-11-11 11:33:52 +0000, WM said:
> 
>>>> 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?
> 
> Cantor said that all rationals are within the sequence and hence within 
> all intervals. I prove that rationals are in the complement.

He said that about his sequence and his intervals. Infinitely many of them
are in intervals that do not overlap with any of your J(n). You have not
proven that there is a rational that is not in any of Cantor's intervals.
Every rational is at the midpoint of one of Cantor's iterval.

-- 
Mikko