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

On 1/25/25 6:07 AM, WM wrote:

On 24.01.2025 13:29, Richard Damon wrote:

no finite set of numbers is teh full set of the Natural Numbers.

 But only finite sets can be used as individuals.

But every FISON and Natural Number IS finite.
I guess you are now just admitting every time you mention ALeph_0 or Omega, you are in error, as those are infinite things, and thus can't be used individually.
Or, are you saying that because you the set of Natual Numbers is infinite, you can't use any of its members individually, and thus *ALL* your math it wrong.
All you are doing is proving you don't understand what was said, and don't understand what finite and infinite mean, or how they differ.

The union of all FISONs does not cover ℕ. Otherwise Cantor's theorem would require the existence of a first necessary FISON.

>
Sure it does, but you need to use an INFINITE set of them,

 Give the first necessary FISON which according to Cantor's theorem exists in case that their union is ℕ.

Asking the question just proves your stupidity and the falsity of your logic.
Sorry, you are just proving you are too stupid to do real mathematics, and too stupid to understand your stupidity.
The question is based on a false premise.

 Regards, WM