Re: The set of necessary FISONs

Am Sat, 22 Feb 2025 18:46:25 +0000 schrieb joes:

Am Sat, 22 Feb 2025 19:32:16 +0100 schrieb WM:

On 22.02.2025 19:19, joes wrote:

Am Sat, 22 Feb 2025 19:11:09 +0100 schrieb WM:

On 22.02.2025 15:57, joes wrote:

Am Sat, 22 Feb 2025 15:07:08 +0100 schrieb WM:

On 22.02.2025 14:23, joes wrote:

>

X is a FISON like every finite union of FISONs.

No, X is an obviously infinite union.

There is no actually infinite set of FISONs because there are
never two actually infinite consecutive sets in ℕ.

Why should there?

Try to name the first number of the second actually infinite set
following upon the first actually infinite set. Then you will
understand.

I don't get it. What even should the second set be?

All FISONs have an actually infinite set of dark numbers as
succdessors ∀n ∈ U(F): |ℕ \ {1, 2, 3, ..., n}| = ℵo. This set differs
for every FISON but is not less than ℵo for ay FISON.

So why is the union of inf. many FISONs finite?

There are only finitely many FISONs. Therefore their union is finite
too.