Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 18 Feb 2025 10:14:27 +0100
Organization: A noiseless patient Spider
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In-Reply-To: <41ffe152-335a-46c0-bbf9-7f44bd486e12@att.net>

On 17.02.2025 23:03, Jim Burns wrote:

> In an inductive set with an only.inductive.subset,
> there is no element which,
> upon the removal of it and its priors,
> all the elements -- or even _almost_ all --
> have been removed.

Therefore such proofs are done by induction. They cover all elements.
> 
>> Example:
>> If every human has an end,
>> then the human race need not have an end.
>> If every human has ended,
>> then the human race has ended.
> 
> If each human ends
> but, a day after they end, another has not ended,
> then the human race does not end.

If every human has ended, then there is no other one.
> 
> If there is a baton (named 'Bob') such that
> each human receiving Bob passes it to
> a human who ends a day or more after they end,
> then,

Bob passes with the last one.

> After all passes, Bob isn't.
> Infinity isn't finite.
> It isn't even almost finite.

Nevertheless: If all elements of a set have been omitted, then the set 
has been omitted.

Regards, WM