Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

Am Mon, 30 Dec 2024 09:40:11 +0100 schrieb WM:

On 29.12.2024 23:45, Moebius wrote:

Am 29.12.2024 um 23:15 schrieb Chris M. Thomasson:

On 12/29/2024 3:09 AM, WM wrote:

 

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

That is not a proof but a silly claim. Believers of such garbage should
be exorcized from public discussions about mathematics.

Your "theorem" is false, Mückenheim. There's a simple counter example:
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.

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

Even better, they are finite (but they do grow).

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

Do you mean the set of numbers less than 100n? I thought you didn’t
believe in the closure of N under multiplication.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.