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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 15:31:00 -0400
Organization: i2pn2 (i2pn.org)
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On 10/20/24 10:26 AM, WM wrote:
> On 20.10.2024 13:56, Richard Damon wrote:
>> On 10/20/24 3:48 AM, WM wrote:
> 
>>> All doubled numbers result in larger numbers. That cannot be avoided.
> ´
>> But since there isn't a "largest" number,
> 
> There is completeness.
> 
> Regards, WM

Which meaning of "Completeness" do you mean?

You do understand that it has been proven that mathematics can't be 
"complete" in the sense that it can prove all true statements?

For set theory, the "Completeness" of the Natural Numbers says there is 
a suprema of the set, and that is the value omega, it just isn't IN the 
set, and completeness doesn't require it to be in it.

Not all infinite sets have a suprema or infima within them, so your talk 
of "completeness" doesn't actualy DO anything without explanation.