Editing Vector space (section)

===Ordered pairs of numbers===
A second key example of a vector space is provided by pairs of real numbers {{mvar|x}} and {{mvar|y}}. The order of the components {{mvar|x}} and {{mvar|y}} is significant, so such a pair is also called an [[ordered pair]]. Such a pair is written as {{math|(''x'', ''y'')}}. The sum of two such pairs and the multiplication of a pair with a number is defined as follows:{{sfn|Jain|2001|p=[https://books.google.com/books?id=-lzAee3uQtIC&pg=PA11 11]}}
<math display="block">
 \begin{align}
 (x_1 , y_1) + (x_2 , y_2) &= (x_1 + x_2, y_1 + y_2), \\
 a(x, y) &= (ax, ay).
\end{align}
</math>

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