A paradox stating that the faster runner can never catch a slower runner because he is forever arriving at a point the slower runner has just vacated. The arguement is attributed to the 5th-century BC Greek philosopher Zeno. The paradox concerns a race between the fleet-footed Achilles and a slow tortoise. The two start moving at the same moment, but if the tortoise is initially given a head start and continues to move ahead, Achilles can run at any speed and will never catch up with it.
Zeno’s argument rests on the presumption that Achilles must first reach the point where the tortoise started, by which time the tortoise will have moved ahead, even if but a small distance, to another point; by time Achilles traverses the distance to his latter point, the tortoise will have moved ahead to another, and so on.
The description of the race is taken from Encyclopaedia Britannica.