An ordered pair, denoted (a, b), is a pair of objects in which the order is significant, so that (a, b) differs from (b, a) whenever a and b are different; this contrasts with the unordered pair {a, b}, which always equals {b, a}. Ordered pairs are also called 2-tuples or sequences of length 2, and the entries of an ordered pair can themselves be ordered pairs, allowing the recursive definition of ordered n-tuples, such as defining the triple (a, b, c) as (a, (b, c)). In an ordered pair (a, b), the object a is called the first entry or first component and b the second, and Cartesian products and binary relations, including functions, are defined in terms of ordered pairs.
Facts
Origin YearFelix Hausdorff proposed an independent definition the same year; Kazimierz Kuratowski 1921 definition is the one most textbooks use today, per the same article. Connections
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Attributed To
Source Ordered pair (Wikipedia)
In Branch
Sources
1. Ordered pair (Wikipedia)
Wikimedia FoundationLead section
In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant.
Wiener definition section
Norbert Wiener proposed the first set theoretical definition of the ordered pair in 1914:
Attributed To: Kazimierz Kuratowski, Article text
One of the most cited versions of this definition is due to Kuratowski (see below) and his definition was used in the second edition of Bourbaki's Theory of Sets, published in 1970.
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