 In the absence of D\(_{\textrm{uncomp}}\) a very different approach was required and Church, Post and Turing each used more or less the same approach to this end (Gandy 1988). First of all, one needs a formalism which captures the notion of computability. Turing proposed the Turing machine formalism to this end. A second step is to show that there are problems that are not computable within the formalism. To achieve this, a uniform process U needs to be set-up relative to the formalism which is able to compute every computable number. One can then use (some form of) diagonalization in combination with U to derive a contradiction. Diagonalization was introduced by Cantor to show that the set of real numbers is “uncountable” or not denumerable. A variant of the method was used also by Gödel in the proof of his  first incompleteness theorem.