Re: The set of necessary FISONs

On 25.01.2025 15:16, Richard Damon wrote:

I said:
Sure it does, you just need to take the union of an infinite number of them.

But that is impossible because there are not two consecutive actually infinite sets in ℕ. Since every FISON is followed by an actually infinite set, ∀n ∈ U(F(n)): |ℕ \ {1, 2, 3, ..., n}| = ℵo, there is no actually infinite set of FISONs.

FISONs enumerate themselves. There is no infinite FISON and hence no infinite number of them.

 Then, what is the highest FISON?

That depends on the system. All we know is that it is finite.

 If there is only a finite number of them, THEN there is a maximum

A variable maximum, "something becoming, emerging, produced, i.e., as we put it, the potential infinite." [Hilbert]
Regards, WM