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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 4 Feb 2025 11:11:29 +0100
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On 03.02.2025 20:48, Jim Burns wrote:
> On 2/3/2025 1:36 PM, WM wrote:

>> Therefore Peano, Zermelo, or v. Neumann
>> create ℕ as well as the set of all FISONs
>> for use in set theory.
> 
> Axioms describe.
> Magic spells create.

To describe something it must be existing. If ℕ is existing, we do not 
need axioms.

>> Therefore all FISONs can be removed from
>> the set of all FISONs.
> 
> We can describe the removal of all of them, sic: {}

We can do it by induction: Remove F(1) and if you have removed F(n), 
remove F(n+1).
> 
>> All natural numbers can be added by induction to a set A.
> 
> Either all natural numbers are in A,
> or they aren't all in A.
> Those are all the choices.

Nonsense. Sets can be added and subtracted.  We can add the set ℕ to the 
set { } by adding 1, and if n has been added, then n+1 is added.

>> 1 is added to A, and
>> if n is added to A, then n+1 is added to A.
> 
>> All FISONs can be subtracted from the set of all FISONs
>> by the same procedure.
>> F(1) is subtracted.
>> If F(n) is subtracted, then F(n+1) is subtracted.
> 
> For each FISON,
> there is a larger FISON not larger than U{FISON}

When the set is subtracted by induction, nothing remains.

> We could decide that  that isn't their behavior,
> but, if we decide that, everything turns to gibberish.

Peano constructs by induction the set ℕ: If we add the set that contains 
1 and with n also n+1, to { }, then we get ℕ.
If we subtract from ℕ the set that contains 1 and with n also n+1, then 
only { } remains. Same holds for FISONs. Therefore: if U(F(n)) = ℕ, then 
{ } = ℕ.

Regards, WM