It's been a long time since I had my Theory of Computation class, but as I recall, the proof that there are computationally undecidable questions uses the same

It's been a long time since I had my Theory of Computation class, but as I recall, the proof that there are computationally undecidable questions uses the same diagonalization technique[1] used to demonstrate that the real numbers are not countably infinite. The same technique can be used to show there are still computationally undecidable questions if you have a Turing Machine with an Oracle. This proof technique suggests not only are there undecidable questions, there are uncountably many of them. Even if you have an Oracle. [1] c.f. http://en.wikipedia.org/wiki/Cantors_diagonal_argument http://en.wikipedia.org/wiki/Cantors_diagonal_argument