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An apparent paradox proposed by the Greek philosopher Zeno around 425 BCE.

Suppose, said Zeno, that Achilles and a tortoise decide to run a race. Since Achilles is a buff Greek mythical hero type dude, and the tortoise is, well, a tortoise, Achilles can run ten times as fast as the tortoise. Consequently, Achilles gives the tortoise a ten yard lead.

Now the race begins. In the time that it takes Achilles to cover the distance to the tortoise's original position, the tortoise has moved another yard forward. When Achilles covers that yard, the tortoise moves forward 1/10 of a yard. Achilles covers that distance, the tortoise has moved forward 1/100th of a yard. Clearly, the tortoise is constantly staying ahead of Achilles. How, then, can Achilles ever overtake the tortoise?

This paradox was not sucessfully resolved until the mid 17th century, when the Scottish mathematician James Gregory demonstrated that an infinite series can have a finite sum.

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