Re: The set of necessary FISONs

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.

 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.

 

The erroneous step is from „every finite number”
to „an infinite number”.

>
Induction proves an infinite number.

 Induction is valid without any infinite sets.

Induction creates infinite sets.
If i contruct x(1) and from x(n) follows x(n+1) then the set of all x(n) is infinite.

In ST+F, there are no infinite sets,
but there is induction.

I apply mathematics.
Regards, WM