The Problem of Achilles Overtaking the Tortoise

Physics does not deal in finite numbers of points, it deals in distances. What achilles can or cannot do is not deduce from mathematics. It depends only on what the relevant laws of physics say. If they say he will overtake the tortoise in a given time, then he will. He just presumed that the mathematical notion that happens to be called infinity faithfully captures the distinction between finite and infinite. That is simply false.