If x,y, and z are three vectors in Rn we have:
a. d(x,y)≥0 for all x and y.
b. d(x,y)=0 if and only if x=y.
c. d(x,y)=d(y,x) for all x and y.
d. d(x,z)≤d(x,y)+d(y,z) for all x,y, and z. Triangle inequality.