Definition:Recursive
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Definition
Function
A function is recursive if and only if it can be obtained from basic primitive recursive functions using the operations of:
a finite number of times.
Set
Let $A \subseteq \N$.
Then $A$ is a recursive set if and only if its characteristic function $\chi_A$ is a recursive function.
Relation
Let $\RR \subseteq \N^k$ be an $n$-ary relation on $\N^k$.
Then $\RR$ is a recursive relation if and only if its characteristic function $\chi_\RR$ is a recursive function.