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

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