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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 20:21:06 +0100
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On 21.11.2024 19:54, Jim Burns wrote:
> On 11/21/2024 11:24 AM, WM wrote:

>> By what is it covered,
>> after all n have been proved unable?
> 
> ⎛ n ↦ i/j ↦ n
> ⎜
> ⎜ (i+j) := ⌈(2⋅n+¼)¹ᐟ²+½⌉
> ⎜ i := n-((i+j)-1)⋅((i+j)-2)/2
> ⎜ j := (i+j)-i
> ⎜
> ⎝ (i+j-1)⋅(i+j-2)/2+i = n

That is not an answer. Further it is only valid for the first numbers 
which are followed by almost all numbers. Never completed.

>> 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.
> 
> I am not enough of a scholar to know
> that this is true of _all_ mathematics, but
> I know that much knowledge of infinity,
> including what I'm most familiar with,
> is grounded in the _finite_

Either limits can be calculated from the finite, or not. If not, then 
Cantor's attempts are in vain from the scratch. If yes, then Cantor's 
attempts have been contradicted.
> 
> Here, I DON'T refer to finite numbers, etc.
> I refer to finite sequences of CLAIMS,
> each of which is true.or.not.first.false.

That is the sequence of claims that limits can be calculated from the 
finite and never the real axis is coloured black.

Regards, WM