Metric Space (S , d) consists of a space S and a fxn d that associates a real number with any two elements of S. The properties of a metric space are:

d(x , y) = d(x , y) forall x,y in S

0 < d(x , y) < inf forall x,y in S & x does not = y

d(x , x) = 0 forall x in S

d(x , y) <= d(x , z) + d(z , y) forall x,y,z in S

I have to show that the Euclidean plane (defined by two 2-D vectors X and Y?) is a metric space.

Havin a bit of trouble with this one...