Re: The set of necessary FISONs

Am Wed, 26 Feb 2025 12:40:13 +0100 schrieb WM:

On 25.02.2025 16:31, joes wrote:

The set of FISONs does not change.

It is the set of definaed natural numbers. It depends on the systemlike
the set of known prime numbers.

Nope. There are inf. many ("defined") FISONs.

I state that induction does not produce actual infinity.

Whatever. Induction does not include infinity, although it does prove
infinitely many formulas containing finite numbers, but not the one
formula saying "all". It is not that strong.

Then consider only the natural numbers which are subject to induction.

Yes, please do that, and not the number Infinity ("all naturals").

I remove by induction all natural numbers. What of ℕ remains in your
opinion?

You cannot remove a non-natural number of elements, such as all of
them.

[blah blah]

The number of naturals is not itself a natural number. So by "removing
every natural" you are removing a non-natural number. Get this?

The other way around: the number of finite elements is infinite.
Anyway, no infinite element is produced.

Right. Zermelo produces all finite elements, no infinite element. So do
I. That is the set.

And the number of these elements is not finite and not an element.

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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.