An example of the second situation is the most famous of the paradoxes of Zeno, the Greek philosopher who lived during the Golden Age of Greece on the island of Elea. Zeno proposed the following "thought experiment". Achilles, a young athlete, runs a race with a tortoise. Achilles can run exactly twice as fast as the tortoise, so to make it fair he gives the tortoise a head start of exactly half the distance from the starting line to the finish line. The starting signal is given and the race begins. Achilles runs to the starting position of the tortoise. In the time it takes to do that, the tortoise has advanced half the distance from his starting position and the finish line. Achilles then advances to the new position of the tortoise. During that time the tortoise again advances half the distance to the finish line. And so on ... Every time Achilles moves ahead by a given distance, the tortoise moves ahead by half that distance. Zeno concluded that Achilles can never catch the tortoise, because in every time interval in which Achilles moves to the tortoise's former position, the tortoise always moves ahead by half that distance
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