Re: The set of necessary FISONs

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”.

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. There is indeed a number, albeit not natural, of FISONs you
can NOT leave out: this number is infinite, and induction doesn’t
reach it.

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

Induction proves an infinite number.

No, it does not prove a sentence to hold for infinite numbers
substituted into it, only finite ones, which there are infinitely
many of.

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.

Sure. But no x is.

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

I apply mathematics.

lol

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.