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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: Wed, 2 Oct 2024 13:10:09 +0200
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On 01.10.2024 22:05, Jim Burns wrote:
> On 10/1/2024 1:29 PM, WM wrote:

>>
>> What is incorrect?
> 
> This is incorrect:
> 🛇⎛ ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  shows that
> 🛇⎜ at no point x
> 🛇⎝ NUF can increase by more than one step 1.
> 
> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  doesn't show that.

You believe that more than one unit fractions can occupy one and the 
same point nevertheless? That would make the distance 0, but it is > 0. 
Therefore you are wrong.
> 
> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0  shows
> ∀n ∈ ℕ: 1/n  >  1/(n+1) > 0
> which shows
> each unit fraction 1/n is not first.

No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 does not prove that n+1 is a natural 
number. Note the infinite sequence
1, 2, 3, ..., ω-2, ω-1, ω.
It consists of infinitely many finite numbers.

Regards, WM