Definition:Set Equality/Definition 2

Definition
Let $S$ and $T$ be sets. $S$ and $T$ are equal both:
 * $S$ is a subset of $T$

and
 * $T$ is a subset of $S$

Notation
This can be denoted in several ways:
 * $S = T \iff \paren {S \subseteq T} \land \paren {T \subseteq S}$

or:
 * $S = T \iff \paren {S \subseteq T} \land \paren {S \supseteq T}$

or:
 * $S = T \iff S \subseteq T \subseteq S$

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

Let $A$ and $B$ be classes.

Also see

 * Equivalence of Definitions of Set Equality
 * Subset Relation is Antisymmetric