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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 7 Sep 2024 10:49:41 -0400
Organization: i2pn2 (i2pn.org)
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On 9/7/24 9:33 AM, WM wrote:
> On 07.09.2024 15:21, Richard Damon wrote:
>> On 9/7/24 9:07 AM, WM wrote:
>>> On 07.09.2024 13:36, Moebius wrote:
>>>  > For all x > 0: NUF(x) = aleph_0 (no "change" at any x)
>>>
>>> Stop that nonsense. ℵo unit fractions and their distances do not fit 
>>> into every interval (0, x). The distance between any pair of unit 
>>> fractions is larger.
>>
>> Of course they do.
> 
> The distance is made of 2^ℵo points. Every x > 0 can mean 3 points.
> 
> Regards, WM
> 


In other words you are just admitting your being stupid.

Every X is just the point itself, not "3 points".

And, there is no reason to add up all the combinations of distances, 
just the ordered set of each unit fraction to its next smaller.

All those add up to less than x, so they fit.

Sorry, you are just proving how stupid your are.