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

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.

 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.

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