In mathematics, an ordered pair is a collection of objects having two coordinates (or entries or projections), such that one can always uniquely determine the object, which is the first coordinate (or first entry or left projection) of the pair as well as the second coordinate (or second entry or right projection). If the first coordinate is a and the second is b, the usual notation for an ordered pair is (a, b). The pair is "ordered" in that (a, b) differs from (b, a) unless a = b.
Cartesian products and binary relations (and hence the ubiquitous functions) are defined in terms of ordered pairs.
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