Re: The set of necessary FISONs

Am Sat, 15 Feb 2025 15:52:06 +0100 schrieb WM:

On 15.02.2025 14:13, FromTheRafters wrote:

WM was thinking very hard :

Each FISON and all its predecessors are proven omissible by
induction. This implies that the whole set is omissible.

Only if there were such a thing as a last FISON being omitted.

You are clearly wrong! Induction concerns the whole set.

Haha. There is no last natural.
You can’t induce over „dark numbers”.

Zermelo: "In order to secure the existence of infinite sets, we need the
following axiom." [Zermelo: Untersuchungen über die Grundlagen der
Mengenlehre I, S. 266]

[actual axiom missing]

This is the axiom of infinity proved by
induction. It ascertains the existence of an infinite set. It ascertains
the set Z, Z_0 and the union of singletons ℕ.

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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.