Prove that the union of two disjoint countable sets is countable This is a question from my proofs course review list that I have had trouble understanding. 
I understand the concept of disjoint sets.  I'm not sure what they mean by countable. How would one prove a set is countable and furthermore, that the union of two countable sets is countable.
Please help me get started with the question by understanding this concept.

There are many ways to prove that set is countable. But the basic method is - enumerate it with some formula.
For example, two disjoint sets
$$A = \{2n-1\mid n-natural\}$$
$$B = \{2n\mid n-integer\}$$
enumerate it
$$A_i=2i-1, i>0$$
$$B_i=2i$$
$A,B$ is countable. I say "$C = A\cup B$ is countable too". Formula will be not so simple as it was before, but it exist and easy to write. 
$$C_i=\begin{cases} {i,i\gt0} \\{2i,i\le0}\end{cases}$$
Prove that every pair of disjoint countable sets gives another countable set in union.
