Ordered pair

A pair (a,b) whose order matters; (a,b)=(c,d) iff a=c and b=d

Ordered pair

An ordered pair is a primitive two-component object $(a,b)$ with the defining equality rule

(a,b) = (c,d)\quad\Longleftrightarrow\quad a=c \text{ and } b=d.

In ZFC , one concrete realization is the Kuratowski definition $(a,b)=\{\{a\},\{a,b\}\}$ (so ordered pairs can be built from sets). Ordered pairs are used to define the Cartesian product , and hence relations and functions .

Examples:

$(1,2)\neq(2,1)$ .
A point in the plane is often modeled as an ordered pair $(x,y)\in\mathbb{R}^2$ .
The graph of a function consists of ordered pairs $(x,f(x))$ .