In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory, stating that, for any set x there is a set y whose elements are precisely the elements of the elements of x. Together with the axiom of pairing this implies that for any two sets, there is a set that contains exactly the elements of both.
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Famous quotes containing the words axiom of, axiom and/or union:
“It’s an old axiom of mine: marry your enemies and behead your friends.”
—Robert N. Lee. Rowland V. Lee. King Edward IV (Ian Hunter)
““You are bothered, I suppose, by the idea that you can’t possibly believe in miracles and mysteries, and therefore can’t make a good wife for Hazard. You might just as well make yourself unhappy by doubting whether you would make a good wife to me because you can’t believe the first axiom in Euclid. There is no science which does not begin by requiring you to believe the incredible.””
—Henry Brooks Adams (1838–1918)
“And thus they sang their mysterious duo, sang of their nameless hope, their death-in-love, their union unending, lost forever in the embrace of night’s magic kingdom. O sweet night, everlasting night of love! Land of blessedness whose frontiers are infinite!”
—Thomas Mann (1875–1955)