In mathematics, an **ordered pair** (*a*, *b*) is a pair of mathematical objects. In the ordered pair (*a*, *b*), the object *a* is called the first entry, and the object *b* the second entry of the pair. Alternatively, the objects are called the first and second *coordinates*, or the left and right *projections* of the ordered pair. The order in which the objects appear in the pair is significant: the ordered pair (*a*, *b*) is different from the ordered pair (*b*, *a*) unless *a* = *b*. This attribute is opposite of unordered pair's attribute: the unordered pair {*a*, *b*} equals the unordered pair {*b*, *a*}.

Ordered pairs are also called 2-tuples, 2-dimensional vectors, or sequences of length 2. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered *n*-tuples (ordered lists of *n* objects). For example, the ordered triple (*a*,*b*,*c*) can be defined as (*a*, (*b*,*c*)), i.e., as one pair nested in another.

Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs.

Read more about Ordered Pair: Generalities, Defining The Ordered Pair Using Set Theory, Category Theory

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