An D5134: Unsigned basic binary operation $d : X \times X \to [0, \infty]$ is a

**metric**on $X$ if and only if

(1) | $\forall \, x, y, z \in X : d(x, z) \leq d(x, y) + d(y, z)$ | |

(2) | $\forall \, x, y \in X : d(x, y) = d(y, x)$ | (D3490: Symmetric function) |

(3) | \begin{equation} \forall \, x, y \in X \left( d(x, y) = 0 \quad \iff \quad x = y \right) \end{equation} |