Re: The set of necessary FISONs

On 12.02.2025 13:08, FromTheRafters wrote:

WM wrote :

On 12.02.2025 01:38, Jim Burns wrote:

On 2/11/2025 2:23 PM, WM wrote:

On 11.02.2025 18:42, Jim Burns wrote:

On 2/11/2025 4:31 AM, WM wrote:

>

The set F of FISONs which can be removed
without changing the assumed result UF = ℕ
is the infinite set F of all FISONs.

>
Yes.

>
Fine.
>

This is proven by just the same induction
as Zermelo proves his infinite set Z.
>
Either you accept both proofs or none.

>
What is this "both proofs"?

>
One is Zermelo's proof by induction that there is an infinite set Z.

 It's an axiom, not a theorem.

Zermelo proves the existence of an infinite set Z by means of the axiom of infinity. The proof fills about one page.
Regards, WM
Regards, WM