A metric on a set X with a function d : X x X \(\rightarrow\mathbb R\) holds for all but one property in the following:
d(x,y)\(\geq 0\forall x,y\epsilon X\)
\(d(x,y) = d(y,m)\forall x,y\epsilon X\)
\(d(x,y)\leq d(x,y) + d(y,z)\forall x,y,z\epsilon X\)
—>> \(d(x,y) = 0 \)whenever \(\neq\) and \(x,y\epsilon X\)
