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

On 9/19/24 7:22 AM, WM wrote:

On 19.09.2024 00:50, Richard Damon wrote:

On 9/18/24 8:33 AM, WM wrote:

On 15.09.2024 23:07, joes wrote:

Am Sun, 15 Sep 2024 21:52:30 +0200 schrieb WM:

>

No definable points, to be precise. If there is no point next to 0 then
there is a gap. I do not accept gaps on the real line.

I.e. „neighbouring” points can’t be defined. There are no gaps.

>
So it is.These points are dark.

>
Nope, they just aren't.
>
To be distinct points, there must be a gap, so they can not be neighboring,

 There are infinitely many points with no extension filling the space.

Right, and none "next" to another, because there is always another in between them.

 

the space is filled by more points, creating smaller and smaller gaps

 That is potential infinity. In actual infinity all points are there at once.

No, that is what infinity actually is. There are not two different "kinds" of it. All the point do exist, and we can express any of them.
Unless your difference is trying to express the difference between Aleph_0 and Omega, but failing.
It seems you are just inventing a term to break your logic system, and you need to figure out what you actually mean by "all are there at once" actually means, since in the potential, all the points are defined.
There are an infinite number of Natural and Rational Numbers. That number is called Aleph_0
There is no highest value for either of these, and the unit fractions, the reciprocal of the Natural Numbers (> 0) thus have no lowest value, or one "next to" 0.
The Infinite Set of these values actually exists, and all the values are in it, so it seems that must be your actual infinity if it is to have any paractical meaning.
If you mean that we, as finite beings, could see all of them "at once" then you are just insane and don't undetstand what infinity actually is and your "actual infinity" just isn't actually infinity.

 Regards, WM
  , that only disappear in the infinite.