21. [4 marks] A set M of natural numbers is Turing-recognizable 1 (we will just say recognizable) if there exists a Turing machine which when given a natural number n as an input, the machine will say YES if n is an element of M. If n/M, the machine will not say YES (it might not halt, or say something else). In other words, the machine is able to recognize the elements in M, but if the input number is not from M, the machine might not be able to confirm that. It will keep looking for the input in M. Prove that: If a set M of natural numbers is recognizable, then there exists a computable function f:NN such that Range (f)=M