Definition:Ordered Pair

Definition
The definition of a set does not take any account of the order in which the elements are listed.

That is, $\set {a, b} = \set {b, a}$, and the elements $a$ and $b$ have the same status - neither is distinguished above the other as being more "important".

Also known as
Some sources call this just a pair, taking the fact that it is ordered for granted.

However, this allows confusion with the concept of a doubleton set, so this usage is not recommended.

In the field of symbolic logic and modern treatments of set theory, the notation $\sequence {a, b}$ is often seen to denote an ordered pair.

This notation is found in many textbooks and journal articles in set theory, including the widely referenced textbooks of and.

In sources where the possibility of confusion is only minor, one can encounter $a \times b$ for $\tuple {a, b}$ on an ad hoc basis.

Also see

 * Equivalence of Definitions of Ordered Pair
 * Equality of Ordered Pairs
 * Definition:Ordered Tuple as Ordered Set


 * Definition:Cartesian Product