How do I prove that a metric space defined by ($A,d$), where $A$ is any set and $d$ is the distance defined by
$\displaystyle d(x,y) = \left\{ 1, \ \text{if} \ x \neq y \atop 0, \ \text{if} \ x = y \right.$
is complete? I know I have to prove that any Cauchy sequence is convergent to a limit, and that the limit must be inside the set, but I don't know how to begin the proof.