Hi there. I'm working with some notions on functional analysis. I have this exercise, which says: Find all the metrics on a set X consisting of two points. So I have this set [tex]X=(x,y)[/tex] (I don't know if this is the right way on defining a set, so I'm just trying). The metric's d which I must find, should accomplish: M1) d is real valued, finite and nonnegative. M2)d(x,y)=0 if and only if x=y. M3)d(x,y)=d(y,x) M4)[tex]d(x,y)\leq d(x,z)+d(z,y)[/tex] So here is the deal, as I have only two points, (x,y) on my set, I think that M4) could never be accomplished, so there are no possible metrics for this set. Is this right?