Re: The set of necessary FISONs

On 17.02.2025 20:59, Jim Burns wrote:

On 2/17/2025 2:27 PM, WM wrote:

Proofs by induction cover all FISONs.

 Proofs by induction prove that
some property A(k) describes each element of
some inductive

set.
Here this property is that FISON F(n) can be removed without changing the premise
U({F(1), F(2), F(3), ...} \ {F(1), F(2), ..., F(n)}) = ℕ. (*)

That reasoning is silent about
whether the _set_ (not its elements) has A(k).

Therefore I gave you an example that you should be able to understand:
If every human has ended, then the human race has ended.
Analogously: If every FISON has been removed without changing the union, then the set {F(1), F(2), F(39, ...} has been removed without changing the union.
Regards, WM