Metric

The Metric System is a common term for the International System of Units.

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In mathematics, a metric (also called distance metric) is an abstraction of the notion of distance; it is used to define metric spaces. The article on metric spaces contains a detailed discussion of the topic.

The mathematical definition of metric follows: Given a set X, a metric d on X is a function X->R satisfying:

1. d(x, x) = 0 for all x in X (alternating) 2. d(x, y) = d(y, x) for all x, y in X (symmetric) 3. d(x, z) <= d(x, y) + d(y, z) for all x, y, z in X (triangle inEquality)

If X is a vector space, any norm |x| on X can be turned into a metric d on X by defining:

d(x, y) := |y - x| , where x, y are in X

See also: Metric tensor