Zeno’s paradox says that, before you can get halfway to your goal, you must get 1/4 way to your goal. Before you can get 1/4 way, you must get 1/8. So on and so forth, creating infinite ‘steps’ that you need to complete before you can get to the end.

It then asserts that this is impossible, because you cannot complete infinite steps.

This assertion is wrong, though, and the “paradox” is proof of it. “Infinite steps” does not mean infinite work – each smaller step is also less work and it never takes any more work than it did when it was just one step.

The answer to Zeno’s Paradox is integral calculus. We know that fleet Achilles catches up and passes the Tortoise in real life. But the idea that you can’t perform an infinite number of smaller and smaller steps in a finite time seems logical.

But this is what integral calculus does: If adds up an infinite number of infinitely small areas to get a reasonable answer. The true formal proof of integral calculus is actually quite complicated and for the serious math geeks only, but there is a great explanation on the Khan Academy website showing why it works.

This video here is a pretty good explanation.

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-1/v/introduction-to-integral-calculus

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