Re: The set of necessary FISONs

joes presented the following explanation :

Am Tue, 25 Feb 2025 10:55:35 +0100 schrieb WM:

On 25.02.2025 10:17, joes wrote:

Am Tue, 25 Feb 2025 10:02:47 +0100 schrieb WM:

On 24.02.2025 19:01, joes wrote:

Am Mon, 24 Feb 2025 15:59:18 +0100 schrieb WM:

These axioms can be applied to show that all FISONs can be removed.

Nope. Any number of them can be removed. Indeed, removing all changes
the union, as you have admitted.

There are not more than any number.

There are more FISONs than any natural number: infinitely many.

Yes potential infinity. There are more FISONs than any fixed natural
number, but the number of FISONs is a natural number

Immediate contradiction: there is no largest natural.
>

because the sequence
{1}
{2, 1}
{3, 2, 1}
...
has no limit.

It does, actually, converge on N.
>

Further induction produces no actual infinity.

WDYM "further"? Induction goes up to infinity.

With von Neumann's construction of ordinals it can be extended to transfinite ordinal numbers. Zermelo's construction cannot be extended this way. I wonder if WM will try Frege next.
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