Ordered -tuple

The ordered -tuple is the ordered collection that has as its first element, as its second element, ... , and as its -th element

In particular, ordered -tuples are called ordered pairs.

Cartesian Product

Let and be sets. The Cartesian product of and , denoted by , is the set of all ordered pairs , where and . Hence

The Cartesian product of the sets , denoted by is the set of ordered -tuples , where belongs to for . In other words

Relation

A subset of the Cartesian Product is called a relation from set to the set . A relation from to itself is called a relation on

See Equivalence Relation, Relations (Mathematics)