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.
Read more about Axiom Of Union: Formal Statement, Interpretation
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)
“It is an axiom in political science that unless a people are educated and enlightened it is idle to expect the continuance of civil liberty or the capacity for self-government.”
—Texas Declaration of Independence (March 2, 1836)
“We must choose. Be a child of the past with all its crudities and imperfections, its failures and defeats, or a child of the future, the future of symmetry and ultimate success.”
—Frances E. Willard 1839–1898, U.S. president of the Women’s Christian Temperance Union 1879-1891, author, activist. The Woman’s Magazine, pp. 137-40 (January 1887)