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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?
Date: Tue, 1 Oct 2024 19:33:09 +0200
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On 01.10.2024 01:07, Richard Damon wrote:
> On 9/30/24 2:54 PM, WM wrote:

>> NUF(0) = 0 and NUF(1) = ℵo. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 shows that at no 
>> point x NUF can increase by more than one step 1. It is fact with your 
>> set too. I am not responsible. I only made the discovery.
> 
> Actually, it shows that at no point CAN it increase by 1.

Wrong because it cannot start with ℵo.
> 
> For any finite number x, NUF(x) will be Aleph_0, and Aleph_0 when you 
> attempt to "increment" it, doesn't change.

If NUF is ℵo at all x > 0 then it must count ℵo unit fractions at 0. Wrong.
> 
> Since there is no finite value of x where NUF(x) can be 1

Wrong presupposition.

Regards, WM