Il. Achilles and the Tortoise

In a race between Achilles and a tortoise where the tortoise has a head start of a certain distance, the faster Achilles wall never overtake the tortoise because he must first reach the point where the tortoise started, and then the point the tortoise had reached when he reached its starting point, and so on. In order for Achilles to go through all these points in this way, he must perform an infinite sequence of acts.