Explain the concept of a recursively enumerable set.

Explain the concept of a recursively enumerable set.

A recursively enumerable set, also known as a computably enumerable set, is a set of natural numbers that can be effectively enumerated by a Turing machine. In other words, a set is recursively enumerable if there exists an algorithm or a Turing machine that can list all the elements of the set, although it may not halt for elements that are not in the set. This means that for any element in the set, the Turing machine will eventually output it, but for elements not in the set, the Turing machine may either halt without outputting them or continue indefinitely without halting.