Re: how

Le 23/06/2024 à 19:58, Jim Burns a écrit :

On 6/22/2024 5:30 PM, WM wrote:

The union cannot be larger than all its FISONs.

 The union cannot be smaller than any FISON.

Agreed. Therefore the union is a FISON.

Each FISON is smaller than another FISON,

The sequence of FISONs is potentially infinite. There is no last one. The end is evolving. It runs through ℕ but never covers a substantial part.

Yes,
the set of FISONs necessary to yield ℕ is empty.

That proves that ℕ is more than all FISONs.

 U{FISON}  is the union of the set of
both necessary and unnecessary FISONs

The unnecessary FISONs can be removed.
According to Cantor's theorem B the set of necesary FISONs must have a smallest element.
Can you understand? Do you agree? Do you have objections?
This proves that ℕ is not the union of FISONs.
Can you understand? Do you agree? Do you have objections?
Regards, WM