ZENO'S PARADOX

PRONUNCIATION: (ZEE-noz PAR-uh-doks)

MEANING: noun:
1. Any of various paradoxes proposed by Zeno, dealing with change and motion.
2. The appearance of getting closer and closer to a goal, but never reaching there.

ETYMOLOGY: After the Greek philosopher Zeno of Elea (c. 490-430 BCE) who proposed a number of paradoxes as defense of the doctrine of his teacher Parmenides.

NOTES: The best-known among Zeno’s paradoxes is that of a race between Achilles and a tortoise. Achilles runs faster, but the tortoise has a headstart. By the time Achilles reaches the tortoise’s starting position, the tortoise has moved forward. By the time he reaches the tortoise’s new position, the tortoise has moved farther, even though the gap is now smaller.

According to the paradox, Achilles would never catch up with the tortoise because the tortoise would always be a little ahead, no matter how small the gap. Yet, we know Achilles does catch up with the tortoise (he is Achilles, not a hare). How does he do it? By not dozing off in his high school calculus and understanding the concept of limits: if you add up that infinite sequence of increasing smaller spans he traveled, you get a finite distance.
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ZEN'S PARADOX - What is the sound of one hand clapping?

ZERO'S PARADOX - division, in the field ℝ of real numbers

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