Why do holomorphic functions separate points?

Question

I have just started looking into complex manifolds and in particular Stein manifolds. Stein manifolds are defined to be both holomorphically convex and holomorphically separable.

It is claimed in many books that every domain in $\mathbb{C}^n$ is holomorphically separable. In other words, for any two points $z,w$ in a domain $D \subset \mathbb{C}^n$ there exists a function $f \in H(D)$ such that $f(z) \neq f(w)$.

For some reason, I can't see it. Can someone point out the obvious thing that I'm missing here.

Cheers.

Answer 1

The coordinate functions are holomorphic.