Definition:Euclidean Metric/Real Number Line

Definition
Consider the Euclidean space $\struct {\R^n, d}$.

On the real number line, the Euclidean metric can be seen to degenerate to:
 * $\map d {x, y} := \sqrt {\paren {x - y}^2} = \size {x - y}$

where $\size {x - y}$ 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