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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
Lines: 32
Message-ID: <vfotg8$15r9a$1@dont-email.me>
References: <vb4rde$22fb4$2@solani.org>   <vf7mqj$1d3m4$2@dont-email.me> <062a0fa5-9a15-4649-8095-22c877af5ebf@att.net> <vf8itt$1hosd$2@dont-email.me> <b1e5a319-eaec-44d2-b961-f90bc241e7e6@att.net> <vf8r7k$1jnia$2@dont-email.me> <d316baa3-de5b-4644-86ff-beacad9df107@att.net> <vfd97u$2jtos$1@dont-email.me> <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <vfe5d5$2olom$1@dont-email.me> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <vfg07k$1chpe$1@solani.org> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <vfgil3$38pn6$1@dont-email.me> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me> <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org> <vfjg9h$3rjvp$2@dont-email.me> <vfkqlr$3fii$1@solani.org> <vfl8o7$3mnmt$4@i2pn2.org> <vflfq9$f82l$1@dont-email.me> <vflovl$1fpr2$3@solani.org> <vfm2m5$iasq$1@dont-email.me> <vfnmo3$ui6v$1@dont-email.me> <vfo5rf$1178s$1@dont-email.me> <vfoqqr$14lcc$2@dont-email.me>
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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.