 wherein the first argument \(i\) represents the position of the function \(\alpha_i(x,y)\) in the prior list. For fixed \(i,n,m \in \mathbb{N}\) it is thus possible to effectively compute the value of \(\alpha(i,n,m)\) by first constructing the definition of \(\alpha_i(x,y)\) and then evaluating it at \(n,m\). But it is also easy to see that \(\alpha_{i+1}(x,x)\) will eventually dominate \(\alpha_i(x,x)\) for sufficiently large \(x\). This in turn suggests that \(\alpha(i,x,y)\) cannot be defined by a finite number of applications of the primitive recursion scheme and is thus not itself primitive recursive.