I have quite a naive question, which doesn't really go deep into physics/mathematics.. :) Let's take seriously the idea that space is continuous. The questions is, how are we able to move in such a space? We know that in a continuous space (real numbers), between two points there are infinitely many other points. That's true for any two points, no matter how close they are, and this seems to be a kind of a paradox. It seems to me that we have to impose a cut off, i.e. the existence of a smallest number that below which you cannot go, since in that case between two points there will be only finitely many points to cross, not infinitely many, hence motion will be in principle possible. Does this make any sense? EDIT: (I rephrase the problem in a more proper way, so if anyone wants to attack an approach, prefer the following one:) The problem can be also rephrased in this way: You are sitting on a mathematical point x0 and you want to move. Motion means that you want to go from x0 to x1, where x1 is the next mathematical point. So the question is, what is the next mathematical point? The answer is, since space is assumed to be continuous, there is no next mathematical point. The exact next point can only be x0 itself, since, if you choose any point x other than x0, you can always find another point y that is closer to x0 than x is. Hence motion is not possible. If the problem is rephrased this way, you can simply ignore all these proofs that involve convergence series thinking that they have solved the problem.