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

On 09.09.2024 21:43, Jim Burns wrote:

On 9/9/2024 2:44 PM, WM wrote:

The unit fractions
  before x > 0 and before x′ > 0
vary.
For both x and x′, they are ℵ₀.many,
but not the same ℵ₀.many.

The same ℵ₀ many are existing in both cases, in addition there are finitely many further unit fractions.

 

and require a minimum length d.

 No.
There is a greatest.lower.bound 0
but there isn't  a _minimum_

There is a minimum larger than a distance of countably many points.

so
each d > 0 is not.minimum.

A d of of countably many points is less than the minimum.
Do countably many points exist as a subdistance of every distance of uncountably many points, like the gaps between two unit fractions?
Regards, WM