Actual Infinity in Reality?

[polymath257]

1.)  Please be more precise: exactly what process do we use to go from 0 to 1? Be specific.

2.)  But yes, at any point there is another point to go through. And yes, we manage to go through all of them.

3.)  The problem is that you are assuming we cannot compete an infinite process. Look at my comments on the definition of 'infinity' above.

1. )  In this case, we are cutting in half the distance between the current position and the end position.  Which you agree, will never result in a number greater or equal to the end positions correct?  In actuality, I believe that one would need to proceed through each point, between 0 and 1 sequentially.  The dichotomy method of half marks allows us an abbreviated way to move forward, to systematically show an infinity and show that we that the end (1) will never be reached.

2.)  If they are without end... how do you go through them all?   That is the question.    (And if you are going to say time again, then how does that help you to get to 1 if X<Y<1.... More or less time, does not help you complete this sequence, it's not a matter of completing it in a timely manner).

3. Using the same method, that you use to show an infinity, also shows that you cannot complete that infinity (hence the concept and the term).   If you disagree with Zeno.... then where?   You agreed to the premises including the math.  Do you think that the conclusion doesn't follow that if X<Y<1  ad infinitum then an infinite number of halfway marks cannot be crossed, therefore the path can never be fully completed?  If so why?

1. The end (1) isn't reached *in that sequence*, but it is still reached. We get out of that sequence after a finite amount of time. Again, you assume we cannot go through an infinite collection of steps. We do because there are also infinitely many times.

2. We 'go through them all' by having, for each real number between 0 and 1 (inclusive, this time), a corresponding time when we go through it. And that is the case: for each real number, we have a corresponding time when we are at that real number. We also have a time when we at at 1. The fact that we go through an infinite number of times is what allows us to go through an infinite number of places. That is why motion is possible.

3. We have completed that infinity when we get to 1. And since there is a time when we get to 1, we have completed that infinity at that point.

I agree that there are an infinite number of points to go through. But I also think we do, in fact, go through them all. In fact, we have gone through all of them by the time we reach 1. Your assumption is that they cannot be crossed, when each and every one of them *is* crossed at some time.