ABSTRACT
The theorem on unique decomposition into prime factors shows that different sequences have different codes. Since there is an algorithm for decomposing a number into prime factors, this coding is effective. This chapter shows that some functions and relations associated with this coding are recursive. To do this, it gives definitions of these functions and relations which show that they are recursive. The chapter takes functions to be total, even when it is only interested in them for certain arguments. It also shows that an inductive definition is called a course–of–values inductive definition.
