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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions?
Date: Wed, 02 Oct 2024 07:30:42 -0400
Organization: Peripheral Visions
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WM pretended :
> 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.

Omega minus one or two is undefined and n plus one closure is 
axiomatic.