# Intuition for the term “separable” in separable metric space

A metric space is separable if and only if it has a countable dense set.

I find this name unintuitive because I can't see how the above definition relates to the notion of separating a space. There is a connection to Hausdorff spaces, which intuitively can be regarded as separated or separable in a way: A separable Hausdorff space has cardinality at most $2^{\mathfrak c}$. This doesn't help me very much, though.

So why are such spaces called separable?