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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: Thu, 21 Nov 2024 17:24:51 +0100
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On 21.11.2024 16:39, Jim Burns wrote:
> On 11/21/2024 5:21 AM, WM wrote:

>> That means the function describing this,
>> 1/10, 1/10, 1/10, ...
>> has limit 1/10.
>> That is the quotient of
>> the infinity of black intervals and
>> the infinity of all intervals.
> 
> The Paradox of the Discontinuous Function
> (not a paradox):

It is a paradox that only 1/10 of the real line is covered for every 
finite interval (0, n] but all is covered completely in the limit. By 
what is it covered, after all n have been proved unable?
> 
> lim.⟨ rc(1), rc(2), rc(3), ... ⟩  ≠
> rc( lim.⟨ 1, 2, 3, ... ⟩ )
> 
> You (WM) do not "believe in"
> proper.superset.matching sets
> discontinuous functions

There is no reason to believe in magic. But if you do, then all 
Cantor-bijections can fail as well "in the infinite". Then mathematics 
is insufficient to determine limits.

Regards, WM