Ordered pair

An ordered pair is a two-component object $(a,b)$ whose equality is componentwise:

In set theory one standard implementation is the Kuratowski ordered pair:

Ordered pairs are used to form the Cartesian product and to encode relations as sets of pairs.

Examples:

• $(1,2)\neq(2,1)$ because the first coordinates differ.
• If $a=b$, then $(a,a)$ is still a well-defined ordered pair (with both coordinates equal).