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From: WM <invalid@no.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 27 Oct 2024 17:15:48 +0100
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Am 27.10.2024 um 14:39 schrieb FromTheRafters:

> If 'not defined' could be a proper subset of the naturals, then there 
> would be a first such 'not defined' in that subset. Of course WM can't 
> substantiate any of his wild claims.

Proof: If infinity is actual, then all elements of the set of unit 
fractions exist. The function NUF(x) = Number of Unit Fractions between 
0 and x starts with 0 at 0. After NUF(x') = 1 it cannot change to 
NUF(x'') =  2 without pausing for an interval consisting of uncountably 
many real points. The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Of 
course x' and x'' are dark rational numbers, the smallest unit fractions.

Regards, WM