Definition:Set Equality

Definition
Two sets are equal if and only if they have the same elements.

This can be defined rigorously as:
 * $S = T \iff \left({\forall x: x \in S \iff x \in T}\right)$

where $S$ and $T$ are both sets.

Axiomatic Set Theory
The concept of set equality is axiomatised in the Axiom of Extension in Zermelo-Fraenkel set theory.