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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Mon, 9 Sep 2024 15:50:40 -0700
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On 9/9/2024 8:01 AM, WM wrote:
> On 09.09.2024 13:47, Richard Damon wrote:
>> On 9/9/24 6:31 AM, WM wrote:
> 
>>> And all gaps are occupied by the unit fractions. Hence every gap is 
>>> too small.
>>
>> But there is always room at the bottom, where the gaps keep getting 
>> smaller
> 
> They all are present from the start. I simply choose a gap that is too 
> small to contain ℵo unit fractions.

Wtf are you talking about? The gaps keep getting smaller:

1/1 - 1/2
1/2 - 1/3
1/3 - 1/4
1/4 - 1/5
1/5 - 1/6
1/6 - 1/7
....

Forever.... They still get arbitrarily close to zero. Don't try to mix 
and match reals with the unit fractions willy nilly. All unit fractions 
are reals, not all reals are unit fractions. See?


>> How can a claim a set of values less then a SPECIFIC NUMBER if I don't 
>> have the number?
> 
> I claim that all unit fractions are existing as real points of the real 
> line. Therefore there is a first one. NUF(x) cannot increase without 
> passing 1 when real points are counted. Your ℵo points cannot exist 
> without including 1, 2, 3 first points.
> 
> Regards, WM
> 
> 
>