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"A Matter of Choice" by Jim Holt. Lingua Franca, November 2001, page 68.
Holt describes the axiom of choice---its history, consequences, misuse, and standing in modern mathematics. The latter third of the article deals with the Banach-Tarski paradox, which states that using the axiom of choice, one can dissect a solid sphere and without stretching the pieces in any way, reassemble those pieces to form two solid spheres each the same size as the original. A consequence of this is that a solid sphere the size of an orange could be dissected and reassembled into a sphere the size of the sun. Pieces of arbitrarily fine detail are needed, so in practice such reassembly is impossible. Holt relates an amusing tale regarding a bet between Princeton mathematicians and the late physicist Richard Feynman. Feynman challenged the above claim about an orange and the sun saying, "...you said an orange, so I assumed you meant a real orange."
--- Mike Breen
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