Re: The set of necessary FISONs

On 1/26/25 3:51 AM, WM wrote:

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.

Why do we need "consecutive" infinite sets, The set of FISONs we are taking the union of are just an infinite subset of the 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.

No, it doesn't exist.
A logic that says it exists as a finite is just WRONG, as you are,

>
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]

Which is about KNOWLEDGE, not the actual existance.
One view of "Potential Infinity" is looking at it as the limit of an infinite sequence of finite sets (none of which ARE the infinite set).
that "variable maximum" is about the composition of the members of that infinite sequence we are looking at.

 Regards, WM