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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Fri, 14 Feb 2025 13:52:27 +0100
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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