Actual Infinity in Reality?

[RoadRunner79]

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.

1.)  So after a certain amount of time has passed, then we jump out of the infinite sequence?  Also, it's not my assumption, you agreed that the math with an infinite number of halves would never reach 1.  Do you still agree with this?

2.)  So if you have an infinite number of times (not infinite amount of time mind you),  then that will make the X in X<Y<1 be equal or greater than 1?   I think you need to be more specific on how this modifies what we previously talked about.  How does time effect X? 

3.)  You are just restating your conclusion as a premise.   The question was... where do you think the error is, in Zeno's statements and logic.   Do you disagree with the premises?   Do you disagree with the math?   Do you think that the conclusion does not follow? 

You may not like the definition of infinite to mean "without inherent limit or without end", however your definition is without end as well .   That is what it means to be infinite and while it make take on a different nuance when dealing with infinite sets, it does change this fact.  You seem to think that a sequence that doesn't end, does end.   And there is your contradiction.  Either it doesn't end and cannot reach the end or it does end, and is not infinite.  You can have it both ways.