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Line 18: The set of ''total recursive functions'' is the subset of partial recursive functions which are [[total function\|total]]. In the [[Church's thesis\|equivalence of models of computability]] the parallel is drawn between [[Turing machine\|Turing machines]] which do not terminate for certain inputs and an undefined result for that input in the corresponding partial recursive function. The unbounded search operator is not definable by the rules of primitive recursion as those do not provide a mechanism for "infinite loops" (undefined values).

General recursive function: Difference between revisions