My definition of recursively enumerable set is that it is the language recognized by some Turing machine.
I want to show that this definition is equivalent to "a r.e. set is the domain of some recursive function". I managed to show that the later implies the former but I have some troubles with the other direction. I just don't see how to start.
Hint: what function is computed by a Turing machine that recognises an r.e. set?