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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: Mon, 28 Oct 2024 10:49:54 +0100
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On 27.10.2024 20:01, FromTheRafters wrote:
> WM pretended :
>> 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:
> 
> Blah blah blah.

Very substantial.

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