Re: The set of necessary FISONs

On 26.01.2025 13:38, Richard Damon wrote:

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,

They would not exist even if they were needed.

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.
 

{1}
{2, 1}
{3, 2, 1}
...
The first column never gets larger than a FISON.

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.

FISONs are about knowledge.
Regards, WM