Re: How many different unit fractions are lessorequal than all unit fractions?

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