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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Sun, 2 Feb 2025 17:34:55 +0100
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On 02.02.2025 13:27, Richard Damon wrote:
> On 2/2/25 6:34 AM, WM wrote:
>> On 02.02.2025 01:33, Richard Damon wrote:
>>> On 2/1/25 1:17 PM, WM wrote:
>>
>>>> The set of FISONs assumed to satisfy U(A(n)) = ℕ cannot be empty. 
>>>> But we can prove by induction that every FISON can be discarded 
>>>> without changing the union. That disproves the assumption.
>>>>
>>> And that is your problem, you make assumptions that are unwarented,
>>
>> I think you've got it! Yes, U(A(n)) is not ℕ.

> But N is in the union of any inifinite set of FISONs.

Then the assumption U(A(n)) = ℕ would not be unwarranted.
> 
> What isn't, is your A(n), as none of the FISONs are individually needed.

But all can be dropped without changing the union.

Regards, WM