metric,
n. 1. a non-negative symmetric binary function defined for a given set, often denoted d(x, y), δ(x, y) or ρ(x, y) and referred to as distance, that satisfies the triangle inequality
and is zero only if x = y. More generally, a pseudo-metric allows δ(x, y) = 0 for x ≠ y; a quasi-metric or skew-metric need not be symmetric, while a semi-metric may fail the triangle inequality. For example, the ordinary distance function in the plane is a metric, since |AB| = |BA|, the triangle inequality follows from Pythagoras' theorem, and |AB| = 0 only if A and B coincide; another metric is
on the continuous real function on the interval [0, 1]. See also metric space. Compare norm, measure. 2. of, using, or pertaining to the metric system.
δ(x, y) + δ(y, z) ≥ δ(x, z).
and is zero only if x = y. More generally, a pseudo-metric allows δ(x, y) = 0 for x ≠ y; a quasi-metric or skew-metric need not be symmetric, while a semi-metric may fail the triangle inequality. For example, the ordinary distance function in the plane is a metric, since |AB| = |BA|, the triangle inequality follows from Pythagoras' theorem, and |AB| = 0 only if A and B coincide; another metric is
sup0≤ x≤1 | f(x) - g(x) |
on the continuous real function on the interval [0, 1]. See also metric space. Compare norm, measure. 2. of, using, or pertaining to the metric system.