Zeno's Paradox - Achilles and the Tortoise

Zeno wrote his paradoxes thousands of years ago - and their philosophic issues are still being discussed today. In Achilles and the Tortoise, he tackles infinity.

Imagine the great, Greek hero Achilles decides to challenge a tortoise to a race. Achilles is a very generous man, and he tells the tortoise that the tortoise can go 100 feet ahead before Achilles will begin to run. So Achilles stands still while the tortoise slowly plods ahead towards the finish line.

When the tortoise hits the 100 feet mark, then Achilles begins to run. He is of course much faster than the tortoise - but the tortoise has not stopped. Whe Achilles is at the 100 foot mark, the tortoise has moved on further ahead - perhaps to 101 feet.

Both of the contestants keep going. Achilles makes it to 101 feet - but by then the tortoise has moved on to 101.5 feet. And on and on - each time Achilles reaches where the tortoise had been, the tortoise will have moved on ahead of that point.

While you would know that it makes sense that Achilles would pass by the tortoise, it would seem by this logic that Achilles should never be able to.

However, with the development of calculus, it was finally shown that even an infinite set of sums like this one can still come up with a finite result - the result showing the number of feet the tortoise travels when Achilles catches up with him and passes him.

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