Source : Free On-Line Dictionary of Computing

Banach-Tarski paradox
     
         It is possible to cut a solid ball into finitely
        many pieces (actually about half a dozen), and then put the
        pieces together again to get two solid balls, each the same
        size as the original.
     
        This {paradox} is a consequence of the {Axiom of Choice}.
     
        (1995-03-29)