Does $d (x,y)= (x-y)^2$ define metric on a set of real numbers? It is a question in functional analysis by writer Erwin Kryzic 

In order for it to be a metric it must follow these properties by definition,
$$d(x,y) \geq 0$$
$$d(x,y)=0 \iff x=y$$
$$d(x,y)=d(y,x)$$
$$d(x,z) \leq d(x,y)+d(y,z)$$
Does it?
