Suppose you start at the origin. You move 1 unit away from the origin to point A. You want to get back to the origin. However you must take a step 1/2 unit away from point A. Each successive step is 1/2 the distance of your previous step. Can you return to the origin in a finite number of steps?
I was thinking something along the line of showing that it is not possible along a straight line path (line segment from A to the origin) and so it is not possible along any other path. However, I feel like something is off in my reasoning.