Original: 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 .
Simplified: A set is called semidecidable ( or recursively enumerable ) , if the algorithm described above can only decide if an element is in the set or is not in the set in finite time , but not both .