Re: The set of necessary FISONs

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.

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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.