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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: Mon, 30 Dec 2024 09:44:48 +0100
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On 30.12.2024 01:36, Richard Damon wrote:
> On 12/29/24 5:31 PM, WM wrote:

>> My theorem: Every union of FISONs which stay below a certain threshold 
>> stays below that threshold.
>> Find a counterexample. Don't claim it but prove it. Fail.

> But what does that prove?

That proves the existence of dark numbers.
> 
> The finite numbers are finite, and that is it.

FISONs do not grow by unioning them. All FISONs and their unions stay 
below 1 % of ℕ.

Proof: Every FISON that is multiplied by 100 remains a FISON that can be 
multiplied by 100 without changing this property.

If ℕ is an actually infinite set then it is not made by FISONs.

Regards, WM