## Computable & Computably Enumerable aka Recursive & Recursively Enumerable

Prove: If $A \subset N$ is computable, then it is also computably enumerable.

I understand that computable (recursive) functions are a subset of computably enumerable (r.e.) functions, but I am not quite sure on how to prove this.

Here's where I'm at: Computable functions are those that when processed by a Turing machine (or some other machine) halt for all input, they do not run forever. Whereas computably enumerable functions are those that when processed by a Turing machine run forever (convergent or divergent) or halt with a correct answer.

So, the domain of each is the same while the range of computable functions is slightly smaller than c.e. functions.

My problem is translating this information into mathematical language and appropriately connecting the dots well enough to call it a proof. Can someone help me with this please and also review my above statements for errors?