Re: The set of necessary FISONs

Am Wed, 12 Feb 2025 16:39:53 +0100 schrieb WM:

On 12.02.2025 12:06, joes wrote:

Am Wed, 12 Feb 2025 10:25:32 +0100 schrieb WM:

 

Zermelo proves the existence of the set Z which contains the infinite
set ℕ of all finite natural numbers.

Pretty sure he doesn’t. What else is in Z?

Consult his Untersuchungen über die Grundlagen der Mengenlehre (1908)
after learning what induction is.

Done and done. As I expected, either Z does not contain, but is equal
to N (the smallest possibility), or it may contain many other things
besides, in which case N among those is not hugely surprising (and
furthermore it would then also contain {N} as an element). Like I said,
N doesn’t contain the *set* of naturals (which would be itself); rather,
it *is* the set of naturals, it contains numbers.

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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.