Example of a space that is separable but not complete

Question

I know that in general metric space $X$ can be separable without being complete. What's a good example?

Answer 1

$\mathbb{Q}$ equipped with the usual Euclidean metric is separable (because it has a countable dense subset: itself), but it is not complete, as we have plenty of sequences of rational numbers converging to irrational limits.

Answer 2

$X= \{1/n:\ n\in\mathbb{N}\}$ with $d(x,y)=|x-y|$ is separable with $X$ countable and dense, but not complete, since $x_n=1/n$ is Cauchy, but not convergent to any element of $X$.