Actual infinities.

[RoadRunner79]

You started by trying to make the distinction in calling it an actual infinity!  Now you are trying to slip away from it?

Have you figured out what your set of infinity is yet (defined it)?
And if you can apply infinity without any distinction are you really describing or saying anything at all?

Here it is:

In the formal language of the Zermelo–Fraenkel axioms, the axiom reads:



In words, there is a set I (the set which is postulated to be infinite), such that the empty set is in I and such that whenever any x is a member of I, the set formed by taking the union of x with its singleton {x} is also a member of I. Such a set is sometimes called an inductive set.

https://en.wikipedia.org/wiki/Zermelo%E2...f_infinity
https://en.wikipedia.org/wiki/Axiom_of_infinity

What I am asking, is not to define what infinity is, nor to prove it as an abstract theory.  But when you are talking about two points, attributing infinity between those two points, what are you describing here?  Infinity of what?

It cannot be related to distance or a physical thing with dimensions, this would lead to a contradiction.  I don't think you can define what is infinite, without making in then finite.  You can potentially make smaller and smaller fractions, but each one will represent a finite amount, and will never get you an infinite result.