Re: The set of necessary FISONs

On 1/26/25 9:24 AM, WM wrote:

On 26.01.2025 13:38, Richard Damon wrote:

On 1/26/25 3:43 AM, WM wrote:

On 25.01.2025 14:59, joes wrote:
>

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

Cantor’s theorem does not force a necessary FISON. We already established
that no finite set of FISONs suffices.

>
Cantor's theorem concerns also infinite sets. Without a first element the set is empty.
>

No, without a first element, the set doesn't exist.

 That is the same.
 Regards, WM
 

Nope. a set not existing is VERY different then the set being an empty set.
The empty set is very specifically a certain set, while a set not existing is something very different.
I guess you are just showing how broken your logic is.
In fact, in the classical set theoretical development of Mathematics, the empty set maps to the number Zero.
Then 1 is the set that contains as its only member the empty set. (which is something different then the empty set itself).
It seems you logic just can't understand how such sets actually work.
Sorry, you are just proving your stupidity.