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

On 01.01.2025 14:51, joes wrote:

Am Tue, 31 Dec 2024 19:05:24 +0100 schrieb WM:

I don't stop but know that every FISON is finite as its name says and
covers at most 1 % of ℕ.

Yes, you stop at some finite threshold.

Go farther. Find a FISON that is not below 1 %.

 

You cannot find a natural number that isn't in a FISON. But there must
be more because FISONs cover less than 1 % of ℕ.

No??? There are infinitely many of them, and together they form N.

Stupid belief. Every union of FISONs which stay below a certain threshold stays below that threshold.
Regards, WM