Metric

A metric is a nonnegative function describing the distance between any two points of a given set. A metric satisfies the triangle inequality

(1)

and is symmetric, so

(2)

A metric also satisfies

(3)

as well as the condition that implies . If this latter condition is dropped, then is called a pseudometric instead of a metric.

A set possessing a metric is called a metric space. On a Riemannian manifold, the metric tensor specifies the Riemannian metric.