achilles and the tortoise - Achilles and the Tortoise; achilles and the tortoise - Argument used by Zeno of Elea to prove the unreality of motion. Achilles runs a race with the tortoise, which is given a certain start. The distance between them consists of an infinite number of parts, which cannot be traversed in any definite time. The tortoise will, therefore, always be a certain distance ahead, since, the moment Achilles reaches the place formerly occupied by it, it will be no longer there. Aristotle pointed out the main fallacy in Zeno's argument. A given distance, even although infinitely divided, does not thereby become infinite but remains a finite distance which can be covered in a finite time.