Let <M1>, <M2>, <M3>, ... be an enumeration of all Turing machines with input alphabet {0, 1}. Let w1, w2, w3, ... be an enumeration of all binary strings. Prove that D = {wi | i ≥ 0 and Mi does not accept wi} is not Turing-recognizable. Hint: Use contradiction—assume D is Turing-recognizable and then use diagonalization.
