Re: The set of necessary FISONs

On 22.02.2025 14:23, joes wrote:

Am Sat, 22 Feb 2025 12:10:12 +0100 schrieb WM:

On 22.02.2025 11:45, joes wrote:

Am Thu, 20 Feb 2025 11:29:26 +0100 schrieb WM:

On 19.02.2025 18:19, joes wrote:

>

If you think UF = X != N, then you need to accept U{} = X.

No. I don't know the relation between a FISON and X.

X is clearly an inductive set, like N.

If X is defined as the true UF (I had overlooked that), then we cannot
apply |X \ {1, 2, 3, ..., n}| = ℵo and then U{} = X does not follow.

Why can you not induce over an inductive set?

Dark numbers.

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.