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

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.

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.

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.
Regards, WM