Definition:Euclidean Metric/Real Number Line

Definition
Consider the Euclidean space $\left({\R^n, d}\right)$.

On the real number line, the Euclidean metric can be seen to degenerate to:
 * $d \left({x, y}\right) := \sqrt {\left({x - y}\right)^2} = \left|{x - y}\right|$

where $\left|{x - y}\right|$ denotes the absolute value of $x - y$.

Also known as
The Euclidean metric is sometimes also referred to as the usual metric.

Also see

 * Definition:Absolute Value