Ok, that's a good point, but it is also true that functions requiring an oracle cannot also be represented in any Turing-complete programming language, right?

Ok, that's a good point, but it is also true that functions requiring an oracle cannot also be represented in any Turing-complete programming language, right? This seems trivial to prove: any function representable in any given programming language maps to a finite string of characters, and finite strings of characters maps to natural numbers.