Metric

Function $\rho(x): X^2 \rightarrow \mathbb{R}_+$ considered a metric if

1. $\forall x, y \in X: \rho(x, y) \geq 0$, and $\rho(x, y) = 0 \iff x = y$
2. $\forall x, y \in X: \rho(x, y) = \rho(y, x)$
3. $\forall x, y, z \in X: \rho(x, z) \leq \rho(x, y) + \rho(y, z)$