2.5.1 Achilles and the Tortoise
Achilles, who is the fastest runner of antiquity, is racing to catch the Tortoise that is slowly crawling a little ahead of him. In order to catch the Tortoise, Achilles will have to reach the place where it presently is. However, by the time Achilles gets there, the Tortoise will have moved to a new location. Achilles will then have to reach this new location. By the time he reaches that location, the Tortoise will have moved on to yet another location, and so on ad infinitum.
Figure 2.1: When the race started the Tortoise (T) was in location (1) that is a small distance (D) ahead of Achilles location (A, 1). By the time Achilles cuts this distance (D), the Tortoise will have moved to a new location (2), and when Achilles reaches this new location (T, 2), the Tortoise will have moved on to yet another location (T, 3), and so on ad infinitum. Achilles will never be able to catch the Tortoise although the distance between them gets ever smaller.