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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Mon, 3 Mar 2025 10:20:20 +0100
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On 03.03.2025 01:42, Richard Damon wrote:
> On 3/2/25 12:51 PM, WM wrote:

> No, it means the set of REQUIRED FISONs is empty, not that we can't use 
> a set of FISONs to make N.

Every set of FISONs which is assumed to be ℕ must have a first element. 
No FISON can serve as such. That is proven by induction.
> 
>> I did: UF = ℕ ==> Ø = ℕ.
> 
> But you didn't. You showed that there are no specific FISON requried to 
> be in that set.

I proved there is no FISON in that set that could be used with more 
reason than a cup of coffee. I did it by induction because then I can 
refer to Zermelo's construction of his potentially infinite sequence of 
numbers Z₀. Of course it follows also directly by
∀n ∈ Z₀: |ℕ \ {1, 2, 3, ..., n}| = ℵo
with Cantor's actually infinite ℕ.

Regards, WM