> [!NOTE] Definition (Ordered pair) > The ordered pair $(x,y)$ is defined to be the set $\{ \{ x \}, \{ x,y \} \}$ which exists by the [[Zermelo Frankel set theory (ZFC)|unordered pair axiom]]. # Applications The [[Cartesian Product|Cartesian product]] of two sets is defined as the set of ordered pairs choosing the first element from the first set.