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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 16:51:18 -0400
Organization: Peripheral Visions
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WM explained :
> On 28.10.2024 15:07, FromTheRafters wrote:
>> WM was thinking very hard :
>
>>> The function NUF(x) = Number of Unit Fractions between 0 and x starts with 
>>> 0 at 0.
>> 
>> Followed by a discontinuity.
>
> No. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 holds everywhere.

Not for n equal to zero.

>>> 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.
>
> It is mathematics:>> 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 holds everywhere if mathematics holds everywhere.
>
>> It doesn't have to happen step by step as you envision it.
>
> As mathematics dictates it.
>
> You have confessed: In order to maintain actual infinity without dark 
> numbers, you have to violate mathematics.

Bull! Just another of your non sequiturs.