Illusions

# 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.

– Vsauce

#### How Many Kinds Of Infininity Are There?

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

– Vi Hart

### 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

Curiosity Staff