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Mind-Bending Math & GamesInfinite Series

Achilles and the Tortoise

Infinitely many steps can take finite time

A sprinter chases a tortoise that has a head start. An ancient argument says he can never catch it. What's wrong with it?

You'll find out

  • Why endless steps can end
  • What endless halves add up to
  • Which shrinking sums never settle

Why it matters

The answer to this old riddle grew into the limit, the idea that calculus is built on.

About 3 min6 interactive slides · 5 questionsLesson 154 · Zone 18

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