Trivial Metric Space Can someone show me how to prove that the trivial metric space is indeed a metric space (if $a=b$ then $d(a,b)=0$ and if $a \ne b$ then $d(a,b)=1$)? 
I'm having trouble with the triangle inequality property.

Hint: You want to prove that
$$d(a,c)\leq d(a,b)+d(b,c)$$
for all points $a,b,c$. For any given points $a,b,c$, just work through the possibilities:


*

*$a=b$ and $b=c$

*$a=b$ and $b\neq c$

*$a\neq b$ and $b=c$

*$a\neq b$ and $b\neq c$


What happens in each case?
