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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? (infinitary)
Date: Mon, 28 Oct 2024 10:07:41 -0400
Organization: Peripheral Visions
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WM was thinking very hard :
> 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,

There need not be any distinction between infinity and your always 
finite but increasing sequence of sets. Infinite means not finite.

> then all elements of the set of unit fractions exist.

They do anyway.

> The function NUF(x) = Number of Unit Fractions between 0 and x starts 
> with 0 at 0.

Followed by a discontinuity.

> After NUF(x') = 1 it cannot change to NUF(x'') =  2 without 
> pausing for an interval consisting of uncountably many real points.

Your "Axiom of because I say so" is overworked.

> The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.

Non sequitur. This is just the second part of your stepwise function. 
It doesn't have to happen step by step as you envision it.

> Of course x' and x'' are 

Blah blah blah.