Re: The set of necessary FISONs

On 14.02.2025 18:43, joes wrote:

Am Fri, 14 Feb 2025 13:52:27 +0100 schrieb WM:

On 13.02.2025 17:38, Jim Burns wrote:

On 2/12/2025 5:19 AM, WM wrote:

>

Induction proves all elements and even the set (Zermelo, Z).

No. Not the set. Each member of the set.

All members of the set.

No, it does not include a member called „all members”.

Induction proves the existence of the inductive set of all its members.
Induction concerns the whole set. Compare Zermelo: "In order to secure the existence of infinite sets, we need the following axiom." [Zermelo: Untersuchungen über die Grundlagen der Mengenlehre I, S. 266] This is the axiom of infinity by induction: { } and with a also a'. It ascertains the existence of an infinite set. It ascertains the sets Z, Z_0 and the union of singletons ℕ.

 

Set intensionality means same.membered sets are one set.
It does not mean sets are self.members.

All members are proved. This means none remains. Zermelo obtains from
that the existence of the infinite set Z.

Wrong.

Read, learn, try to understand.
Regards, WM