Ordered Pair

An ordered pair is a pair of values where the order is significant.^[1] This means that the ordered pair (a,b) may not be the same as the ordered pair (b,a).

Ordered pairs are usually written in the form (a,b). The form <a,b> is sometimes used to avoid conflict with other uses of the notation (a,b). Ordered pairs are used to define the terms function and relation.

The first entry in an ordered pair is the abscissa. The second entry an ordered pair is the ordinate. The plural of abscissa is abscissae. In the ordered pair (4,-2), the abscissa is 4 and the ordinate is -2.

Equality of Ordered Pairs

(a₁,b₁) = (a₂,b₂) if and only if a₁ = a₂ and b₁ = b₂.

Click on the blue point in the manipulative and drag it to change the figure. Note that the ordered pair associated with the point changes depending on where the point is on the graph.

Ordered Triples

An ordered triple is a set of three numbers where order matters. Ordered triples are used, among other things, to define a point in a three dimensional Cartesian space. An example of an ordered triple is (x₀,y₀,z₀).