10.1 Recursive Functions
Recursive function theory gives a mathematical definition of computable numerical functions by specifying basic functions and closure operations that generate increasingly complex functions from simple ones, and this framework allows one to reason about computation purely within arithmetic. All functions considered in this section have inputs and outputs in the natural numbers: $$ \mathbb{N} = {0,1,2,\dots}. $$ An $n$ ary function is written: $$ f : \mathbb{N}^n \to \mathbb{N}, $$...