Editing Axiom of union (section)

== Relation to Intersection ==
There is no corresponding axiom of [[intersection (set theory)|intersection]]. If <math>A</math> is a ''nonempty'' set containing <math>E</math>, it is possible to form the intersection <math>\bigcap A</math> using the [[axiom schema of specification]] as
:<math>\bigcap A = \{c\in E:\forall D(D\in A\Rightarrow c\in D)\}</math>,
so no separate axiom of intersection is necessary. (If ''A'' is the [[empty set]], then trying to form the intersection of ''A'' as
:{''c'': for all ''D'' in ''A'', ''c'' is in ''D''}
is not permitted by the axioms. Moreover, if such a set existed, then it would contain every set in the "universe", but the notion of a [[universal set]] is antithetical to Zermelo–Fraenkel set theory.)