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What is Zeno's paradox?

Learn about Zeno's paradox and its concepts.

Zeno' paradox has puzzled thinkers for years. [©Shutterstock, 2010]
©Shutterstock, 2010
Zeno' paradox has puzzled thinkers for years.

Zeno's paradox was the invention of Zeno of Elea (ca.490-ca.425 B.C.), a Greek philosopher and mathematician. He is famous for his paradoxes that deal with the continuity of motion.

One form of the paradox is if an object moves with constant speed along a straight line from point 0 to point one, the object must first cover half the distance (1/2), then half the remaining distance (1/4), then half the remaining distance (1/8), and so on without end. The conclusion is that the object never reaches point one. Because there is always some distance to be covered, motion is impossible.

In another approach to this paradox, Zeno used an allegory telling of a race between a tortoise and Achilles (who could run 100 times as fast), where the tortoise started running 10 rods in front of Achilles. Because the tortoise always advanced 1/100 of the distance that Achilles advanced in the same time period, it was theoretically impossible for Achilles to pass him.

The English mathematician and writer Charles Dodgson (1832-1898), better known as Lewis Carroll, used the characters of Achilles and the tortoise to illustrate his paradox of infinity.

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