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One of [[Zeno]]'s paradoxes concerns "Achilles and the tortoise." It concerns an imaginary race between the swift warrior Achilles and a slow-moving tortoise, which is given a head start. Although Achilles runs much faster than the tortoise, Zeno argued that Achilles can never actually catch the tortoise. In order to catch him, Achilles must first reach the place where the tortoise started. But by the time Achilles reaches that place, the tortoise will have moved. Even if Achilles has run a hundred feet while the tortoise has moved only one foot, Achilles has not yet caught the tortoise. To catch him, Achilles must again reach the place where the tortoise is now. But, again, by the time he reaches that place the tortoise will have moved. Even though the tortoise moves a smaller distance each time, it seemed to Zeno that Achilles could never actually catch him. In mathematics, the paradox is resolved by observing that the times it takes Achilles to perform each iteration form a [[geometric progression|geometric series]], which has an infinite number of terms but a finite sum.

One of [[Zeno]]'s paradoxes concerns "Achilles and the tortoise." It concerns an imaginary race between the swift warrior Achilles and a slow-moving tortoise, which is given a head start. Although Achilles runs much faster than the tortoise, Zeno argued that Achilles can never actually catch the tortoise. In order to catch him, Achilles must first reach the place where the tortoise started. But by the time Achilles reaches that place, the tortoise will have moved. Even if Achilles has run a hundred feet while the tortoise has moved only one foot, Achilles has not yet caught the tortoise. To catch him, Achilles must again reach the place where the tortoise is now. But, again, by the time he reaches that place the tortoise will have moved. Even though the tortoise moves a smaller distance each time, it seemed to Zeno that Achilles could never actually catch him. In mathematics, the paradox is resolved by observing that the times it takes Achilles to perform each iteration form a [[geometric progression|geometric series]], which has an infinite number of terms but a finite sum.

== See also ==

== See also ==