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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Unit fractions...
Date: Thu, 29 Aug 2024 06:26:35 -0400
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After serious thinking Chris M. Thomasson wrote :
> On 8/28/2024 6:02 PM, Chris M. Thomasson wrote:
>> Just a little plot I did for Moebius and WM using unit fractions on any 
>> line in n-ary space. 3d here...
>> 
>> https://i.ibb.co/9n71tZf/ct-pov.png
>> 
>> https://i.ibb.co/0hXnPpf/ct-pov.png
>> 
>
> Wrt WM. Are his dark numbers, say plotting unit fractions on a line. Okay. 
> Well, they will never hit zero even though they tend to zero. So, are WM's 
> dark numbers the residue between 0 and any unit fraction, so to speak? So, 
> 1/0 is not a unit fraction but 1/(really_large_natural_number) is? Still 
> finite but I was wondering about the dark parts?

They are in his imagination only. He simply "wants" them to exist so 
that he can use them to refute Cantor's diagonal argument about |Q| = 
|N|. He thinks numbers must be identified in order to pair them to show 
a bijection. He also thinks that failing to show a bijection means that 
there is no bijection.