Re: The set of necessary FISONs

Am Sat, 22 Feb 2025 19:02:12 +0100 schrieb WM:

On 22.02.2025 15:03, Richard Damon wrote:

On 2/22/25 7:35 AM, WM wrote:

The inductive step is proved in my example from |ℕ \ {1, 2,
3, ..., n}| = ℵo, i.e., by several axioms, and in Zermelo's example by
a single axiom.

Which just proves that no specific FISON is individually REQURED to
make the set of Natural Numbers.

If every FISON can be omitted, ten nothing remains for a sufficient set.
Because if there was any sufficient set, it would have a first FISON.

Haven't you agreed that omitting everything does change the union?

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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.