This is from an exercise in Boolos' Computability text. My problem is as follows:
I am looking for a method that encode numbers for recursive functions. Then given such an encoding for recursive functions by natural numbers, let d(x) = 1 if the one-place recursive function with encoding number x is deﬁned and has value 0 for argument x, and d(x) = 0 otherwise. Show that this function is not recursive.
I am thinking the actual question is just a diagonalization argument, and it doesn't depend in any way on details of the coding.