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The Axiom of Choice is an axiom of set theory, and states: * From any collection of disjoint, non-empty sets, EQN:A_i,\quad~i=0,\;1,\;\ldots there is a set /C/ containing one element from each EQN:A_i This is slightly controversial, because it is non-constructive. It asserts the existence of the set /C/ without telling you how to construct it. The Axiom of Choice is equivalent to Zorn's Lemma and the Well-Ordering Principle. * http://www.google.co.uk/search?q=axiom+of+choice