The Banach-Tarski Paradox Of Infinite Chocolate

Want to create chocolate out of nothing? It's kinda, sorta possible with the Banach-Tarski Paradox. First, take a chocolate bar that's four squares by eight squares (we know about your candy drawer). Then, crop off the first three squares in column one, then make a horizontal cut towards the top right corner over row four. And finally, cut off the very first square on the left. Re-arrange the remaining chocolate to make a full candy bar. Still with us? Watch the following video to see how you can take away chocolate and still have a full bar. The "magic" involves the mathematics of infinity.

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Uncover The Banach-Tarski Paradox

To understand this paradox, start by asking yourself: "What is infinity?"

How Many Kinds Of Infininity Are There?

In math, all a number needs to be "infinite" is to be bigger than any finite number.

Key Facts In This Video

  1. In math, all a number needs to be infinite is to be bigger than any finite number. 00:09

  2. There is no set of surreal numbers because there are too many to fit in this set. 07:38

  3. Each unique counting number also has a unique prime factorization. 08:45

Written by Curiosity Staff December 30, 2016

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