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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary, effectively)
Date: Sun, 5 Jan 2025 11:45:16 +0100
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On 04.01.2025 19:26, Moebius wrote:

>>>> Every union of FISONs including them all which stay below a certain 
>>>> threshold stays below that threshold.

> I just mentioned a counterexample to your claim,

That is not an example but a silly claim contradicted by my theorem. My 
theorem is proved by the fact that nothing is in the union which could 
make it larger than all elements in the union.
> 

> | For each and every FISON F: F c_proper IN.

Not only finite but below 1 % of |ℕ|.

> But UNION(Set_of_FISONs) = IN.

Every union of FISONs which stay below a certain threshold stays below 
that threshold.

> So the union of (the set of) _all_ FISONs does NOT "stay below" IN, 
> though each and every FISON does.

Your matheologial belief is outside of mathematics and does not deserve 
further discussion.

Regards, WM