One consequence of it is that one can take a sphere of radius one, divide it into five subsets, and recombine then into two spheres of radius one, according to Banach and Tarski.
One consequence of it is that one can take a sphere of radius one, divide it into five subsets, and recombine then into two spheres of radius one, according to Banach and Tarski. Both Cohen and Gödel showed that both it and its denial are consistent with set theory. For 10 points--name this principle first noted by Peano which holds that one can make a new set by taking one element from every set in a collection of sets.
One consequence of it is that one can take a sphere of radius one, divide it into five subsets, and recombine then into two spheres of radius one, according to Banach and Tarski.
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