The Banach-Tarski Paradox is cool.
Of course, I don't really understand how it works, but it's nice to know that, in principle, one can disassemble a golf ball into a finite number of pieces and reassemble it into the planet Jupiter.
*Edit: The little .gif animation on the link at the bottom is friggin' hilarious.*
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"Everything you know is wrong
Black is white, up is down, and short is long
And everything you thought was so important doesn't matter.
Everything you know is wrong
Just forget the words and sing along
All you need to understand is
Everything you know is wrong!"
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Woohoo!
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