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)
“The man whose whole activity is diverted to inner meditation becomes insensible to all his surroundings. If he loves, it is not to give himself, to blend in fecund union with another being, but to meditate on his love. His passions are mere appearances, being sterile. They are dissipated in futile imaginings, producing nothing external to themselves.”
—Emile Durkheim (1858–1917)