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

On 9/10/24 3:10 PM, WM wrote:

On 10.09.2024 14:07, Richard Damon wrote:
 

A GIVEN infinte set of unit fractions will have a total. length of d, but by just removing a finite number of the largest elements, you still have an infinite set, and the size of that new set can be made as small as you want (as long as that value is actually > 0)

 Do countably many points exist as a subdistance of every distance of uncountably many points, like the gaps between two unit fractions?

Yes, you can find countably many points as subdistances, in fact you can find Aleph_0 of them.

  > The size of that new set can be made as small as you want
 Even when the size is only countably many points?

Yes, a countable infinite can have a finite number of elements removed and still be countablye infinite.
Infinites work somewhat differently than finite numbers, as they ae a "degree" above them.

 Regards, WM