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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Wed, 19 Feb 2025 21:23:42 -0500
Organization: i2pn2 (i2pn.org)
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On 2/19/25 11:57 AM, WM wrote:
> Am 19.02.2025 um 13:17 schrieb Richard Damon:
> 
>> Name a FISON that can not be put into a set that is sufficient set, 
>> one whose union is the set of Natural Numbers.
> 
> Every FISON. There is no sufficient set. If it 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.
> 
> Regards, WM
> 

Look up the meaning of sufficient. I don't think you know the meaning of 
the word.

Note, your subject line uses the word you mean, "necessary", but you 
ignore the fact that a set of necessary elements doesn't need to exist.

The fact that you can omit something, doesn't make it not sufficient.

Also, you don't understand what "induction" does, it doesn't MAKE a set, 
it TESTS a set. Of course, it could be that in your Naive logic, you do 
things different, but Naive logic, like Naive Set Theory, is just incorrect.