Distance

A distance is a function $d:X\times X\to {\mathbb{R}}^{+}$ that satisfies, $\forall x,y,z\in \mathbb{X}$

1. $d(x,x)=0$
2. $d(x,y)=0⟹x=y$
3. $d(x,y)=d(y,x)$
4. $d(x,z)\le d(x,y)+d(y,z)$ i.e. the triangle inequality