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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Tue, 22 Oct 2024 20:34:28 +0200
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On 22.10.2024 19:38, Jim Burns wrote:

> The description of each element in ℕ
> requires its double to also be in ℕ

All that is in ℕ, according to your opinion, is accepted. If you find 
that the set ic complete, then it is doubled.
> 
> ...not so different from the way in which
> the description of a right triangle
> requires
> the square of its longest side to equal
> the sum of the squares of the two other sides.

Your above expression is in fact a very closely related one.

Regards, WM