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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: Thu, 31 Oct 2024 18:28:15 +0100
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On 31.10.2024 12:36, Richard Damon wrote:
> On 10/30/24 7:53 AM, WM wrote:

>> NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by 
>> more than 1 at any point x of the real axis.
>>
> Because it grows BETWEEN points on the real axis from 0 to ℵo.

I investigate its behaviour at single points.
> 
> Your problem is there isn't a "first" x > 0 above 0 to see it increase 
> at,

We do not see dark numbers but I can prove their existence by
∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

>  so it can just jump to ℵo.
But it cannot do so at a single point.

Regards, WM