I have known that:
A function $\Bbb N → \Bbb N$ is recursive if and only if its graph is a recursive subset of $\Bbb N^2$.
Now I am considering about the partial functions. Is it the fact that:
A partial function $f:\Bbb N\dashrightarrow\Bbb N$ is partial recursive if and only if its graph is a recursively enumerable subset of $\Bbb N^2$.
If it is true (or one direction is true), may I please ask for a proof? Or some reference would be also appreciate (I searched it but did not obtain any useful result).
Note: It is from a math course (and I have asked in the math site). And I have not learnt about the related things about computer science (for instance, I have not learnt about the Turing machine and I have no skill of coding). So sorry I cannot understand explanations which involves the usage of terms in computer science. May I please ask for a mathematical approch please? Thanks!
I have done some search but I cannot find some helpful material. Any reference would be appreciate to. Thanks a lot.