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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 07:41:10 -0400
Organization: i2pn2 (i2pn.org)
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On 9/9/24 10:53 AM, WM wrote:
> On 09.09.2024 13:32, Richard Damon wrote:
> 
>> No, because the claim is GIVEN an x, we can do "Y", that is make the 
>> Aleph_0 unit fractions below it.
> 
> You are in error. MY CLAIM is: Given ℵo unit fractions smaller than 
> every x > 0, then I choose any of their gaps.

Which mean what?

Given a number, I can pick one?

What does that claim to show?

> 
>> Until you have chosen your x, we don't need to provide those unit 
>> fractions, so, you can't use them to create your x.
> 
> You claim that ℵo unit fractions are smaller than ANY x > 0. That is 
> simply fool's crap.

Why, name the x, and I can name the series of Aleph_0 unit fractions 
smaller than it. I can even write a formula so anyone can do it.

> 
>> To follow YOUR idea, then *YOU* get stuck in the infinite loop of 
>> every time you change your x, the unit fractions change so you need to 
>> change to another x, and the unit fractions change again.
> 
> I do not change anything. There are unit fractions as real points on the 
> real line. These real points are really real and therefore must start 
> somewhere. Hence there is a beginning, one ore more first points.

Why do they need a beginning (at that end)?

Yes, then have ONE beginning, at 1/1, so we can count them, but at the 
other end they do not.

There is a boundry, and that is 0, but that isn't the "first" of them, 
as it is outside the set.

You just don't understand the concept of actually INFINITY.

If there WAS a smallest unit fraction, then there couldn't be an 
infinite number of them, as we could count them down from there.

> 
> Regards, WM
> 
>