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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sat, 15 Feb 2025 18:17:48 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 15 Feb 2025 12:31:28 +0100 schrieb WM:
> On 14.02.2025 18:32, joes wrote:
> 
>> You claim that UF = X and also U({}) = X.
> No. You and others have claimed that there is a set of FISONs containing
> all natural numbers. I have accepted that a s premise.
So what do you claim?

>> If UF=N and N={}, then UF={}.
> No, learn what an implication is!
I understand it perfectly well. You apparently don’t. Ex falso…

> There is no FISON that is in the claimed set. Therefore If UF = ℕ then ℕ
> = {}.
On the contrary, the set of all FISONs contains *all and only* the FISONs.
Nobody but you is saying that the empty set or the union thereof should
equal N.
Get this: We agree with the premise, but not with the implication,
therefore not with the conclusion.

> This does *not* prove UF = {}. F contains sets and UF contains natural
> numbers, but not enough natural numbers, not ℕ.
You could’ve gone right out and said you’re extending N with infinite
numbers.

-- 
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.