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Zeno's Paradox

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Ancient mathematicians did not know the idea of limits, and they devised several paradoxes of endlessness. In Zeno (5th century B.C) paradox, Achilles and the tortoise had a race. Achilles could run 10 times as fast as the tortoise, but the tortoise had a hundred yard start. Achilles runs the hundred yards, but the tortoise is now 10 yards ahead. Achilles runs the 10 yards, but the tortoise is now 1 yard ahead. Achilles runs the 1 yard, but the tortoise is now 1/10 yard ahead, and so on. How can Achilles overtake the tortoise? The ancient Greeks did not know about limits, so in their logic the problem could not be solved. However, we know that 100 +10 +1 +1/10 + 1/100 ... has a limiting sum=(1000/9) and so at this point, Achilles overtakes the tortoise.

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