axiom of union

For any X there exists a set Y=X.

The Axiom of Union is an axiom of Zermelo-Fraenkel set theoryMathworldPlanetmath. In symbols, it reads


Notice that this means that Y is the set of elements of all elements of X. More succinctly, the union of any set of sets is a set. By Extensionality, the set Y is unique. Y is called the union of X.

In particular, the Axiom of Union, along with the Axiom of Pairing allows us to define


as well as the triple


and therefore the n-tuple

Title axiom of union
Canonical name AxiomOfUnion
Date of creation 2013-03-22 13:42:49
Last modified on 2013-03-22 13:42:49
Owner Sabean (2546)
Last modified by Sabean (2546)
Numerical id 8
Author Sabean (2546)
Entry type Axiom
Classification msc 03E30
Synonym union