Although my plan is to strike ball with paddle in the next fraction of a second, Zeno, the paradoxical one, would say that for two reasons I cannot do so: 1) since the ball is frozen motionless at each instant of time, there never is a time when it moves, and 2) even if we do assume that the ball is capable of motion, before it can reach the surface it must travel half of the distance between its present location and the surface, then half of the remaining distance, and so on ad infinitum. Thus the ball will always be travelling and never arrive. (There is never any last segment of halves for it to traverse because an infinite series has no last member.) I proved Zeno wrong by actually hitting the ball, but his arguments are of interest because they highlight theoretical problems which any mathematical theory of motion must be capable of addressing.