Actual Infinity in Reality?

[polymath257]

Let me do it like this. Suppose you are attempting to go through the sequence .9, .99, .999, .9999, .99999, .... There are two scenarios..

In the first, you are at .9 after 1 second, at .99 after 2 seconds, .999 after 3 seconds, etc. I agree that at this rate you will never get through the sequence: it will take an infinite amount of time to do so.

In the second, though, you are at .9 after 1 second, .99 after 1.5 seconds, .999 after 1.75 seconds, .9999 after 1.875 seconds, etc. Each step takes half the time of the previous one. In this scenario, you *will* get through the sequence of 9's after 2 seconds. At the 2 second mark you are past every single one of them.

And yes, whenever you are at any of those points, you have more to go through.
And yes, when you get to t=2, you are past all of them.
And no, there isn't a last one you went through.
And yes, you went through all of them.

The point: you do, in fact, go through an infinite number of times in every finite duration.

Why does this not work when you do the same process that you used to show an infinity, and is also the one in Zeno’s paradox?  You always go to something different and don’t address this in the dichotomy paradox.

Note for everyone else. You may notice, that the math in Zeno’s paradox will never reach it’s goal. If the math gives you trouble, you can see that this same process is being used to show that there is an infinite amount of numbers, that you cannot get to the destination, then you add another infinite, and can then reach the destination. In more ways than one... what is being claimed simply does not add up.

OK, again, part of the problem is the definition of the term 'infinity'. You claim an infinity cannot have an end and that it cannot be bounded. That is simply false. The sequence of 9's above is a wonderful example.

For each one in the sequence, there are an infinite number that are larger. This is true. So it is an infinite collection (whether potential or actual is irrelevant here).

It is also bounded since everything in that sequence is less than 1. Each and every term of that sequence is smaller than 1.

So, we have an infinity that is bounded.

The resolution is easy: we have two different notions of boundedness here. One has to do with where in the e a term is and the other has to do with where in the interval from 0 to 1 that term is. The sequence is unbounded in the first sense and bounded in the second. But they are two different notions of being bounded, so there is no contradiction there.

When you ask if we can 'get through' a sequence, you have to specify exactly what you mean. Strictly speaking there isn't even a process here. There are two collections: the terms of the sequence and the numbers between 0 and 1. Both are infinite. You don't get to 1 by staying in the sequence. But that isn't relevant if you want to get to one from within the numbers between 0 and 1.

But we *do* get to the destination, which means we *do* go through all those points. If you deny that, exactly which point do we not go through? At which point does the division break down?