Re: The set of necessary FISONs

On 02.02.2025 13:27, Richard Damon wrote:

On 2/2/25 6:34 AM, WM wrote:

On 02.02.2025 01:33, Richard Damon wrote:

On 2/1/25 1:17 PM, WM wrote:

>

The set of FISONs assumed to satisfy U(A(n)) = ℕ cannot be empty. But we can prove by induction that every FISON can be discarded without changing the union. That disproves the assumption.
>

And that is your problem, you make assumptions that are unwarented,

>
I think you've got it! Yes, U(A(n)) is not ℕ.

But N is in the union of any inifinite set of FISONs.

Then the assumption U(A(n)) = ℕ would not be unwarranted.

 What isn't, is your A(n), as none of the FISONs are individually needed.

But all can be dropped without changing the union.
Regards, WM