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

On 9/10/24 3:07 PM, WM wrote:

On 10.09.2024 13:59, Richard Damon wrote:
 

It isn't an "opaque cloud" that stops them from having a smallest, but a infinite accumulation of values at that bound (that is outside the set).

 One or finitely many or a cloud. More is not available.
 Regards, WM

But NONE is still an option
If you allow your "cloud" to have extent, then you can have your cloud.
So a cloud of all Aleph_0 unit fractions below x, exist in the range
(0, x)
But that is just punting the problem, as that cloud doesn't have a smallest element, and all the values are still distinct and are not your "dark" numbers, as all of the members are usable individually and are defined.