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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 27 Oct 2024 18:15:55 +0100
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Am 27.10.2024 um 17:07 schrieb WM:

> course x' and x'' are [...] rational numbers, the smallest unit fractions.

Really?

Hint: If x' is a unit fraction then 1/(1/x' + 1) is a unit fraction 
which is smaller than x' and if x'' is a unit fraction then 1/(1/x'' + 
1) is a unit fraction which is smaller than x''. So neither x' nor x'' 
can be "the smallest unit fraction".