Re: The set of necessary FISONs

On 26.02.2025 13:22, joes wrote:

Am Wed, 26 Feb 2025 13:04:10 +0100 schrieb WM:

On 26.02.2025 12:53, joes wrote:

Am Wed, 26 Feb 2025 12:40:13 +0100 schrieb WM:

On 25.02.2025 16:31, joes wrote:

>

The set of FISONs does not change.

It is the set of definaed natural numbers. It depends on the
systemlike the set of known prime numbers.

Nope. There are inf. many ("defined") FISONs.

Defining is a human activity. Never an infinity will be defined.

They have, by the power of induction. (Infinity itself has been
defined separately.)

The power of induction proves
∀n ∈ U(F): |ℕ \ {1, 2, 3, ..., n}| = ℵo

Right. Zermelo produces all finite elements, no infinite element. So
do I. That is the set.

And the number of these elements is not finite and not an element.

He ascertains the set.

The *set* is not in the set.

No, why should it? But the set is proven to exist by induction.
Regards, WM