Ordered pair

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In mathematics, an ordered pair (a, b) is a pair o mathematical objects. The order in which the objects appear in the pair is signeeficant: the ordered pair (a, b) is different frae the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.)

Ordered pairs are an aa cried 2-tuples, or sequences o length 2; ordered pairs o scalars are an aa cried 2-dimensional vectors. The entries o an ordered pair can be ither ordered pairs, enablin the recursive defineetion o ordered n-tuples (ordered leets o n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as ane pair nested in anither.

In the ordered pair (a, b), the object a is cried the first entry, an the object b the seicont entry o the pair. Alternatively, the objects are cried the first an seicont coordinates, or the left an richt projections o the ordered pair.

Cartesian products an binary relations (an hence functions) are defined in terms o ordered pairs.