How to prove that something forms a base topologically speaking

[snesnerd]

Homework Statement

If $(X,d)$ is a metric space. I want to show that the set of all open balls and $\emptyset$ form a base.

Homework Equations

The Attempt at a Solution

I know that we need to show that the union of all these sets (or balls) is the whole set. I feel like this is simple yet, I am unsure what to write so that I do not miss any important facts.

 

[micromass]

Can you start by giving the definition of a base and the properties you need to show?