Show that the Hilbert space $l^2$ equipped with the standard inner product and induced norm is separable (contains a countable, dense subset). I am thinking about using the subset of rational numbers. I believe this is countable and dense in R but I am not sure how to show this in $l^2$- unless it is the same?
Note: $l^2$ is the vector space of all sequences {$x_n$} in a field F such that $\sum_{k=1}^\infty |x_k|^2 < \infty$.