 Definition 1.2: A function \(f:\mathbb{N}^k \rightarrow \mathbb{N}\) is general recursive if there is a system of equations \(\mathcal{E}(\psi_1,\ldots,\psi_n,\vec{x})\) such that if \(\psi^k_i\) is the leftmost functional symbol in the last equation of \(\mathcal{E}\) then for all \(n_1,\ldots,n_k, m \in \mathbb{N}\)