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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