A semimetric on a set $X$ is a function $d\colon X\times X\to \R$ which satisfies:

1. $d(x,y)\geq 0$
2. $d(x,y)= 0$ if and only if $x=y$ ;
3. $d(x,y) = d(y,x)$ .

A semimetric differs from a metric in that the triangle inequality is not required to hold.