> [!definition] > > Let $X$ be a [[Set|set]] and $d: X^2 \to \real^+$ be a mapping, then $d$ is a **pseudo-metric** if > 1. $d(x, y) = d(y, x)$ for all $x, y \in X$. > 2. $d(x, z) \le d(x, y) + d(y, z)$ for all $x, y, z \in X$.