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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 28 Jan 2025 07:45:29 -0500
Organization: i2pn2 (i2pn.org)
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On 1/28/25 3:58 AM, WM wrote:
> On 27.01.2025 18:10, joes wrote:
>> Am Mon, 27 Jan 2025 15:33:01 +0100 schrieb WM:
> 
>>> Also an infinite set needs a first element.
>> No problem, any infinite set of FISONs has one.
> 
> But no set of FISONs the union of which is ℕ has a first element. If an 
> infinite set was existing, you could easily find a first not completely 
> useless element. Try it!
> 
> Regards, WM
> 

Many sets of FISONs whose union is N exist, and each of those sets has a 
first element.

Your set, which doesn't exist, that has no first element, is the set of 
FISON required to form that N.

The fact that any finite number of the set of FISONs isn't needed, 
doesn't make the set whose union is N undefined, only the attempt to 
define a minimal set of them.

This is just in the nature of infinity, and you err by trying to 
manipulate the infinite as if it was finite, which just blows your logic 
to smithereens.