Computably enumerable set

In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable, provable or Turing-recognizable if: There is an algorithm such that the set of input numbers for which the algorithm halts is exactly S. Or, equivalently, There is an algorithm that enumerates the members of S. That means that its output is a list of all the members of S: s1, s2, s3, ... . If S is infinite, this algorithm will run forever, but each element of S will be returned after a finite amount of time.

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