A class of total functions is a PRC class if:
- The class includes all projection functions $p_i(x_1,\ldots,x_n) = x_i$ and the initial functions $n(x) = 0$ and $s(x) = x+1$.
- The class is closed under composition and primitive recursion.
Prove that the class of all total functions is a PRC class.
Is it true if I say every total function is computable? And then say because the class of computable functions is a PRC class, so is the class of total functions.