The set of all finite subsets of $mathbb{R}_+$ is countable.

I’m struggling to figure out how to prove that the set of all finite subsets of $mathbb{R}_+$ is countable. I thought that it wasn’t but a TA told me it was and I need to prove why it’s countable. I don’t even know how to start this proof.
If it helps, I solved this problem with $mathbb{Z}_+$ by saying when writing down first several subsets of $mathbb{Z}_+$, you can clearly see a pattern that can be enumerated.