Intuitively, a recursive function may be defined as an integer-valued function of one or more integer variables which may be computed by a definite algorithm. In order to produce a rigorous definition, one may proceed long at least two approaches; one may define the notion of algorithm rigorously in order to complete the intuitive definition given above or one may proceed inductively, first declaring certain functions to be recursive and then specifying definite procedures by which one may construct any other recursive function starting from the initial set. In this entry, we shall concentrate on the latter approach, only making a few brief remarks regarding the former approach towards the end.
with the initial condition
is a recursive function.
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