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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: Tue, 10 Sep 2024 22:01:01 -0400
Organization: i2pn2 (i2pn.org)
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On 9/9/24 11:15 AM, WM wrote:
> On 09.09.2024 16:32, Python wrote:
>> Le 09/09/2024 à 12:19, Prof. Dr. Mückenheim, aka WM a écrit :
> 
>>> ℵo unit fractions cannot fit into one of the ℵo intervals between two 
>>> of them.
>>
>> (O, x) is NOT an interval between two unit fractions.
> 
> 1/n - 1/(n+1) = x is an interval between two unit fraction. This 
> interval is shifted to the origin, yielding the interval (0, x). It does 
> not contain ℵo unit fractions. It does not contain 1/n.

Of course it contains aleph_0 unit fractions, but yes, 1/n isn't one of 
them, but you can remove any finite number of unit fractions from the 
set and still have aleph_0 of them.

> 
> Note that unit fractions are points on the real line. Therefore there is 
> a beginning. How many unit fractions can be smallerorequal than all unit 
> fractions. This question proves the existence of a smallest unit fraction.

Nope. Try to name it.

There are NO unit fractions smaller_or_equal to ALL unit fractions, as 
there isn't a smallest.

Your logic is just breaking your brain.

> 
> Regards, WM