Example of an uncountable metric space where every point is isolated

Question

I was trying to come up with an example of an uncountable metric space all of whose points are isolated. I've had difficulty thinking of one, has anyone got any nice examples?

Just in case:

Definition: a point $x \in M $ is not isolated if for everly $\varepsilon > 0$ there is a $y \in M$ such that $0< d(x,y) < \varepsilon$.

Answer 1

Real numbers with the discrete metric. I.e. $d(x,y) = 1$ if $x \neq y$.