IIRC, In "The Emperors New Mind" Penrose mentions that Godel employed Cantor's "Method of Diagonalization" to show that within a system such as the natural numb

IIRC, In "The Emperors New Mind" Penrose mentions that Godel employed Cantor's "Method of Diagonalization" to show that within a system such as the natural numbers there can be true statements(uncountably infinite) not on the list of provable statements(countably infinite).