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What are some interesting mathematical paradoxes?

What I have in mind are things like the Banach-Tarski paradox, Paradox of Zeno of Elea, Russel's paradox, etc..

Edit: As an additional restriction, let us focus on paradoxes that are not already in the list at:

https://secure.wikimedia.org/wikipedia/en/wiki/Category:Mathematics_paradoxes

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    You mean other than the ones in https://secure.wikimedia.org/wikipedia/en/wiki/Category:Mathematics_paradoxes ?2010-08-09
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    Yes, that is a very useful restriction to add. Sorry, I realize that my question is too broad as it stands.2010-08-09

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