View source for Ordered pair

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{{MSC|03E}}

A construct $(a,b)$ of two objects $a$ and $b$ in which order is significant; $(a,b)$ is not the same as $(b,a)$ unless $a=b$.  Equality between ordered pairs is defined by
$$
(a,b) = (c,d) \ \Leftrightarrow \  a=c \wedge b=d \ .
$$

A realisation in terms of [[axiomatic set theory]] is to write
$$
(a,b) = \{ \{a\} , \{a,b\} \} \ .
$$

Given sets $A$ and $B$ the set of all ordered pairs $(a,b)$ with $a \in A$ and $b \in B$ is the [[Cartesian product]] $A \times B$.

====References====
* P. R. Halmos, ''Naive Set Theory'', Undergraduate Texts in Mathematics, Springer (1960) ISBN 0-387-90092-6