ABSTRACT
This chapter shows that the class of recursive functions has certain closure properties; i.e., that certain operations performed on members of the class lead to other members of the class. It uses these results to see that various functions are recursive. The class of recursive functions is closed under composition. A class of functions is recursively closed if it contains the initial functions and is closed under composition, inductively closed. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.
