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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Tue, 31 Dec 2024 10:49:16 -0500
Organization: i2pn2 (i2pn.org)
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On 12/31/24 4:36 AM, WM wrote:
> On 31.12.2024 06:08, Moebius wrote:
>>  Andernfalls handelt es sich lediglich um unbewiesene und oft genug 
>> auch falsche Behauptungen (so wie in diesem Fall)
>>
>>> For each and every FISON F: F c_strict (WM: "below") IN. But the 
>>> union of all FISONs is not c_strict (WM: "below") IN but = IN.
> 
> Yes. Only a real fool could claim that by unioning the gap between less 
> than 1 % and ℕ could be closed.
> 
> Every FISON is less than 1 % of ℕ because by expanding it by a factor 
> 100 the situations remains the same - forever.
> 
> Gruß, WM
> 

No, the problem is you always stop before you get to the end of unioning 
EVERY FISON, as you always have a stopping point.

The problem is infinity doesn't have an end, so you can't get to it by 
individual finite steps that can't be processed without end. THus, your 
"logic" jsut fails to have the needed tools to handle, or even create, a 
infinite set.

Your logic doesn't HAVE the full set of the Natural Numbers, or EVERY 
FISON, because it doen't have the ability to actually generate an 
infinite set, so your claims that you can't "undo" an infinite set are 
just spurious, and based on your exploded to smithereens by 
contradiction "logic".