Re: The set of necessary FISONs

On 2/5/25 2:18 PM, WM wrote:

On 05.02.2025 19:43, Jim Burns wrote:
 

It might just matter what a natural number, induction,
a FISON, and a union are.

 The axiom of induction:∀P( P(1) /\ ∀k(P(k) ==> P(k+1)) ==> ∀n (P(n)))
 P(1): U(F(n) \ F(1)) = ℕ.
 P(k): U(F(n) \ {F(1), F(2), ..., F(k)}) = ℕ
==>
P(k+1): U(F(n) \ {F(1), F(2), ..., F(k+1)}) = ℕ.
 Regards, WM

And thus you can claim that no F(n) is "necessary".
Doesn't mean you can't use a set of them to build the set of Natural Numbers.
Unless you want to admit that you logic says we can't factor 36, since none of its factors are "necessary" in such a factoring.