ACIT4330-Page/content/Definitions/Metric Spaces/Metric Space.md

Definition

A Metric on a set X is a function d : X \times X \to [ \, 0, \infty \rangle such that

1. d(x,y) = d(y, x), \; \forall x,y \in X
2. d(x, y) = 0 \iff x = y
3. d(x,z) \leq d(x,y) + d(y, z) (think of this as a triangle and Pythagoras' Theorem) Think of d(x, y) as the distance between x and y.