(from the article `mathematics, foundations of`) ... 2 if and only if = 0 or = 1, where 0 is the empty set and 1 is the set consisting of 0 alone. Both definitions require an extralogical axiom to ... ...a set, S, which contains all and only the subsets of S.Union axiom. If S is a set, then there is a set containing all and only the m...

Found on http://www.britannica.com/eb/a-z/a/132

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