Re: The set of necessary FISONs

On 1/26/25 7:39 AM, WM wrote:

On 26.01.2025 12:11, joes wrote:

Am Fri, 24 Jan 2025 10:37:51 +0100 schrieb WM:

 

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 the existence of a necessary set.

 But your claim that a set exists forces the existence of a first FISON that cannot be discarded. Otherwise all can be discarded.
 Regards, WM
 

It isn't MY claim that a set of necessary FISION exist, it is YOURS.
My claim is that the set of Natural Numbers exist, as it has been shown.
If we start with the *INFINITE* set of FISONs (and the size of that set IS infinite) we can remove any finite combination of them and their union will be the Natual Numbers.
I make no claim that there is a specific set of "necessary" FISONs, just am able to show that *ANY* infinite set of them will include all Natural Numbers. Note, you can even exclude an infinite subset of FISONs from that infinite set, as long as it still leaves an infinite set, and you will cover the full set of Natual Numbers.
Your logic is just built on error, and shows that you are just ignorant of what you are talking about, and so ignorant that you can't see you ignorance.