Just like the runner who competes against the turtle, running ten times as fast, but the turtle has ten feet advantage and the runner's never going to overtake it. Why? In the time it takes the runner to make the ten feet, the turtle's already run another foot, and until the runner has made this foot, it's again a tenth of a foot ahead. The runner runs this thenth foot, but the turtle has already made another hundredth of a foot... - so we see, the runner can only come infinitely close to the turtle, but never overtake it
(Please don't take this as a confession that Schrödinger's Cat may never even have caught the mouse!)