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→The Axiom of Choice
===The Axiom of Choice===
===The Axiom of Choice===
Before continuing to a complete proof, we must discuss the [[Axiom of Choice]]. The axiom states than given any collection of sets (possibly infinitely many sets - possibly uncountably many sets!), there exists a set which contains exactly one element of each.
===The Banach-Tarski Construction===
===The Banach-Tarski Construction===