[Reincarnate]

This is an example of Zeno's Paradox. It's basically a way of asking "if we can divide some finite distance into infinitely many pieces, then how can we possible make it from one end to the other? There are INFINITELY many pieces to traverse!"

It's not really a paradox -- the question just sounds confusing because of the way it's phrased and because people tend to have a hard time grasping infinity. In this case, the fact that you're talking about a finite distance already solves the problem.

Say we drop the ball 10 feet. To traverse 10 feet, you have to first traverse 5. But to traverse that, you need to travel 2.5 feet, and so forth. Ultimately we can keep going until we ask ourselves the question, "How can anything move at all? To travel some distance X we have to travel some distance smaller than X first, but to travel that we need to travel something even shorter than that, etc."

The problem lies in the sort of assumption that adding up an infinite number of terms equals infinity. Some infinities are "larger" than others. There is technically no such thing as "the number infinity." Infinities only make sense when you speak of limits, and when we're talking about limits, we're really talking about rates.

Even with a fully continuous underlying space, Zeno's Paradox still fails. An infinitesimal amount of distance may be infinitely small, but it isn't nothing.

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I also want to point out to you guys: There's a ***HUGE*** difference between quantizing space and making space discrete. You don't need to invoke discrete space to solve this problem.