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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 15 Feb 2025 17:38:06 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 15 Feb 2025 15:55:55 +0100 schrieb WM:
> On 15.02.2025 14:40, Richard Damon wrote:
> 
>> And since you build your claimed "set" by Naive Set theory, your sets
>> are worthless.
> Zermelo constructs his set in modern set theory. Induction concerns the
> whole set. Compare 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] 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.
>> 
>> The set you show is empty, is the set of FISONs that are individually
>> not necessary.
> The remaining set should have at least one element.
Indeed, if you remove any number of FISONs, infinitely many remain.

-- 
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.