Definition:Metric Space/Triangle Inequality

Definition
Let $M = \struct {A, d}$ be a metric space, satisfying the metric space axioms:

Axiom $M2$ is referred to as the triangle inequality, as it is a generalization of the Triangle Inequality which holds on the real number line and complex plane.

Also see

 * Reverse Triangle Inequality:
 * $\forall x, y, z \in X: \size {\map d {x, z} - \map d {y, z} } \le \map d {x, y}$