metric space

In mathematics, a metric space consists of a set $X$ , the “space,” for which the distance between all of it’s members can be calculated using a function $d$ , the metric.

$d$ must be a real function defined on $X^2$ , and for each $x,y,z \in X$ the following must all be true:

$d(x,y) > 0$ and $d(x,y) = 0 \iff x = y$ (non-negative, identity of indiscernibles)
$d(x,y) = d(y,x)$ (symmetry)
$d(x,y) \leq d(x,z) + d(z,y)$ (triangle inequality)