stylistic:tone, structural:scholar_edition
Ordered pairs of numbers

A second key example of a vector space is provided by pairs of real numbers x and y. The order of the components x and y is significant, so such a pair is also called an ordered pair. Such a pair is written as (x, y). The sum of two such pairs and the multiplication of a pair with a number is defined as follows: (x 1, y 1) + (x 2, y 2) = (x 1 + x 2, y 1 + y 2), a (x, y) = (a x, a y). {\displaystyle {\begin{aligned}(x_{1},y_{1})+(x_{2},y_{2})&=(x_{1}+x_{2},y_{1}+y_{2}),\\a(x,y)&=(ax,ay).\end{aligned}}}

The first example above reduces to this example if an arrow is represented by a pair of Cartesian coordinates of its endpoint.