This is a paradox that has been bothering me since I was taking algebra in high school. Let's say that I want to represent the distance between to objects. Given that numbers are infinite in both directions, by which I mean that there is no limit to how large, or small a number can be, there should be no limit to how close, or how far to objects can be from each other. Lets say I were to drop a a ball from a distance of one foot above my desk, the ball will move towards my desk, and the number representing the distance between the ball and the desk will become increasingly smaller until it comes into direct physical contact with the desk, at which point the ball will be a distance of 0 inches from the desk. however this should be mathematically impossible. The number representing the distance between the desk and the ball should just keep getting smaller and smaller, never actually reaching zero. Mathematically, no matter how close the ball gets, it can still get closer without touching. even if you were to represent the distance as a decimal followed by 100 googul zeros with a 1 at the end, you can still add one more zero, or another 100 googul for that matter. clearly however, there is a point at which a physical distance may not become any smaller, and the two objects must touch. In fewer words, there are infinite numbers between any two numbers, no matter how close or far apart those two numbers are, thus in the one foot between the ball and the desk, there should be infinite points in space, and in order for the ball to reach the desk it must pass through every point in space between the two objects. how can the ball pass through every point if there are infinite points?