ABSTRACT
Imagine a race between a runner named Achilles and a tortoise. The tortoise is given a head start of some distance, and they both start at the same time. Achilles must, of course, first cover the distance between the starting line and the tortoise’s starting point, but during that time the tortoise will have moved ahead a bit; then Achilles must cover the distance between the tortoise’s starting point and the point to which the tortoise has moved, during which time the tortoise will have moved ahead a bit further; and so on and so on. Whenever Achilles reaches the point at which the tortoise was, the tortoise will have moved a bit further ahead, so though Achilles will continue to narrow the distance between himself and the tortoise, he will never catch up to the tortoise. But surely that can’t be right!
