## Ordered pair |

in

, anmathematics **ordered pair**(*a*,*b*) is a pair of objects. the order in which the objects appear in the pair is significant: the ordered pair (*a*,*b*) is different from the ordered pair (*b*,*a*) unless*a*=*b*. (in contrast, the {unordered pair *a*,*b*} equals the unordered pair {*b*,*a*}.)ordered pairs are also called

, or2-tuples (sometimes, lists in a computer science context) of length 2; ordered pairs ofsequences are also called 2-dimensionalscalars . the entries of an ordered pair can be other ordered pairs, enabling the recursive definition of orderedvectors (ordered lists of*n*-tuples*n*objects). for example, the ordered triple (*a*,*b*,*c*) can be defined as (*a*, (*b*,*c*)), i.e., as one pair nested in another.in the ordered pair (

*a*,*b*), 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. andcartesian products (and hencebinary relations ) are defined in terms of ordered pairs.functions - generalities
- informal and formal definitions
- defining the ordered pair using set theory
- category theory
- references

In **ordered pair** (*a*, *b*) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (*a*, *b*) is different from the ordered pair (*b*, *a*) unless *a* = *b*. (In contrast, the *a*, *b*} equals the unordered pair {*b*, *a*}.)

Ordered pairs are also called *n*-tuples*n* objects). For example, the ordered triple (*a*,*b*,*c*) can be defined as (*a*, (*b*,*c*)), i.e., as one pair nested in another.

In the ordered pair (*a*, *b*), 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.