I'm just refreshing my memory on Turing machines and computability, and I was wondering how to design a function of 2 arguments that is guaranteed not to be computable. I've seen the proof (by diagonalization) for one argument functions, and I'd like to make sure I have the right idea. For functions with 2 arguments, a sketch of my proof is as follows:
Let f_{1},f_{2}... be a listing of all 2 argument Turing computable functions
Let d be a 2 place function (and assume that it is Turing computable) such that d(x,y)=1 if the xth function in the list of Turing computable functions returns 0, and return 1 otherwise. Then d is not in our list of functions, but it was assumed that it was. Therefore, d is not a computable function of 2 arguments. Sorry for the lack of latex, hopefully this is understandable without it for now.