High Quality Content by WIKIPEDIA articles! In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A set which is not computable is called noncomputable or undecidable. A more general class of sets consists of the recursively enumerable sets. For these sets, it is only required that there is an algorithm that correctly decides when a number is in the set; the algorithm may give no answer (but not the wrong answer) for numbers not in the set.

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