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Ah yes, Zeno's paradox.
The problem: The conclusion that you can never get where you're going doesn't fall logically from the fact that every distance, no matter how small, can be halved. While Zeno points out that you have to cover "half of" each distance, it doesn't consider that you actually *do* cover those distances.
Otherwise, one could just as easily say that every distance, no matter how long, can be doubled and thus you can never stay where you are.
Always an interesting thought, though.