 Thus it is shown that no more general definition of effective calculability than that proposed above can be obtained by either of two methods which naturally suggest themselves (1) by defining a function to be effectively calculable if there exists an algorithm for the calculation of its values (2) by defining a function \(F\) (of one positive integer) to be effectively calculable if, for every positive integer \(m\), there exists a positive integer \(n\) such that \(F(m) = n\) is a provable theorem. (1936a [BE: 121])