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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 20 Oct 2024 07:56:05 -0400
Organization: i2pn2 (i2pn.org)
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On 10/20/24 3:48 AM, WM wrote:
> On 20.10.2024 00:54, Jim Burns wrote:
>> On 10/19/2024 2:19 PM, WM wrote:
> 
>> A doubled finite is finite.
> 
> If all finites are doubled, then not all results can be in that set.
> Either more finites appear, or the results are infinite.
>>
>> No k exists such that
>> 2⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.
> 
> All doubled numbers result in larger numbers. That cannot be avoided.
> 
> Regards, WM

But since there isn't a "largest" number, we can find that in the set.

It doesn't work for finite sets, but does for infinite sets, something 
that seems to blow your mind to smithereens.