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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 7 Nov 2024 11:24:32 +0200
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On 2024-11-06 17:52:01 +0000, WM said:

> On 06.11.2024 15:59, Mikko wrote:
>> On 2024-11-05 11:26:58 +0000, WM said:
>> 
>>>   Cantor's results are
>>>> conclusions of proofs and you have not shown any error in the proofs.
>>> 
>>> I have. This example for instance proves that he did not enumerate all 
>>> rationals, because the rationals are dense, the intervals are not dense.
>> 
>> You have not proven that. It is fairly easy to prove that there are
>> no positive rationals other than those enumerated by Cantor (if I
>> recall correctly he enumerated only positive rationals). To prove
>> that there are positive rationals that are not included in Cantor's
>> enumeration it suffices to show one but you have not shown any.
> 
> I have shown that without rational numbers outside of the intervals 
> with irrational endpoints covering 3 of infinitely many units the real 
> axis has measure 3.

No, you have not shown it, only said.

-- 
Mikko