Actual Infinity in Reality?

[RoadRunner79]

Well, I explained my reasoning for a last point (it's not an assumption).  Even with only two points on a segment if we start at zero and end at A, then zero would be the last point before A.  With more than one point and progression to A through these points, you will have a last point.  It is not dependent on time at or between points, as long as there is some sort of movement towards the destination.

However If you are not going to engage, and just keep repeating the claim, then I'm not going to repeat myself..... Now after numerous posts you admit that this process which shows your infinite points also prevents you from reaching the destination at all.  There is some mystery process which is added, and allows us to end the other process, which is being defined as infinite (without end or limit).    If you have something new to talk about, or wish to engage with something that I have said... I'm happy to discuss.   Otherwise I'll leave the last word to you if you desire.

And if there are only finitely many points between, then there will be a last point. But if there are infinitely many, there does not have to be. That is simply one of the ways infinite sets differ from finite ones: infinite ones need not have a first or last.

The underlying assumption you seem to make is that an infinite number of steps cannot be finished. But they can, *if* they are done faster and faster, so that the total time is still finite.

So, the difficulty seems to be that an infinite sum of positive quantities can be finite. it is easy to see that they can be bounded. For example:

.9
.99
.999
.9999
.99999
...

I think you will agree that there are infinitely many numbers in this list (whether potential or actual). But, clearly, every number on this list is smaller than 2.

So this infinite set (potential, if you like) is bounded above by 2.

This is an example of an infinite, but bounded collection. Even if you only want to do 'potential' infinities, the numbers that appear are ALL smaller than 2 (and, in fact, each is smaller than 1).

So, even with a potential infinity, it is possible to be infinite and bounded. It is infinite in quantity, but finite in terms of size of the numbers involved.

And, if these represent time passage, we DO go through all of them and reach 1. Not by staying in this sequence, but by going through the sequence in a finite time.

You may do things as fast or slow as you like.   In Zeno's dichotomy paradox, and your X<Y<1    no matter how much time, you will never reach 1, you will always have another point to go through that is less than 1 (hence why the term infinity applies). This is not an assumption... this is the math function being described!  The argument is not that it will take an extraordinary amount of time to complete!