Definition:Set Equality/Definition 1

Definition
Let $S$ and $T$ be sets. $S$ and $T$ are equal they have the same elements:


 * $S = T \iff \paren {\forall x: x \in S \iff x \in T}$

Otherwise, $S$ and $T$ are distinct, or unequal.

Equality of Classes
In the context of class theory, the same definition applies.

Let $A$ and $B$ be classes.

Also see

 * Axiom:Axiom of Extension


 * Equivalence of Definitions of Set Equality