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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Wed, 19 Feb 2025 17:03:46 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 19 Feb 2025 17:52:38 +0100 schrieb WM:
> Am 18.02.2025 um 19:22 schrieb Jim Burns:
>> On 2/18/2025 10:22 AM, WM wrote:
> 
>> You (WM) have located a problem.
>> You try to work around it by not.mentioning it.
>> What you're not.mentioning is your assumption that none of these sets
>> are infinite.
> Wrong. Induction has been invented for infinite sets.
> Um aber die Existenz "unendlicher" Mengen zu sichern, bedürfen wir noch
> des folgenden ... Axioms. [Zermelo: Untersuchungen über die Grundlagen
> der Mengenlehre I, S. 266]
Go on not mentioning it.

>> ⋃{F} = ℕ
> Proof: If UF = ℕ is assumed, then F(1) can be omitted without changing
> the union of the remainder. And if F(n) can be omitted without changing
> this union, then also F(n+1) can be omitted without changing this union.
> That makes the omitted FISONs the inductive collection of all FISONs and
> proves the implication: If UF = ℕ, then { } = ℕ.
Disproof: UF != {}

-- 
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.