Ordered Pair - Generalities

Generalities

Let and be ordered pairs. Then the characteristic (or defining) property of the ordered pair is:

The set of all ordered pairs whose first entry is in some set X and whose second entry is in some set Y is called the Cartesian product of X and Y, and written X×Y. A binary relation between sets X and Y is a subset of X×Y.

If one wishes to employ the notation for a different purpose (such as denoting open intervals on the real number line) the ordered pair may be denoted by the variant notation