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In mathematics, an ordered pair is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair is different from the ordered pair unless a = b.
Ordered pairs are also called 2-tuples, or sequences of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors. The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples. For example, the ordered triple can be defined as ], i.e., as one pair nested in another.
In the ordered pair , 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 components, the first and second coordinates, or the left and right projections of the ordered pair.
Cartesian products and binary relations are defined in terms of ordered pairs.