Re: The set of necessary FISONs

On 03.03.2025 01:42, Richard Damon wrote:

On 3/2/25 12:51 PM, WM wrote:

No, it means the set of REQUIRED FISONs is empty, not that we can't use a set of FISONs to make N.

Every set of FISONs which is assumed to be ℕ must have a first element. No FISON can serve as such. That is proven by induction.

 

I did: UF = ℕ ==> Ø = ℕ.

 But you didn't. You showed that there are no specific FISON requried to be in that set.

I proved there is no FISON in that set that could be used with more reason than a cup of coffee. I did it by induction because then I can refer to Zermelo's construction of his potentially infinite sequence of numbers Z₀. Of course it follows also directly by
∀n ∈ Z₀: |ℕ \ {1, 2, 3, ..., n}| = ℵo
with Cantor's actually infinite ℕ.
Regards, WM