Simple set
In computability theory a simple set is an example of a set which is recursively enumerable but not recursive.
Definition
A subset S of the natural numbers N is called simple if it satisfies the following properties
- N\S is infinite
- S is recursively enumerable
- S ∩ X ≠ ø for any infinite recursively enumerable set X
Properties
- The set of simple sets and the set of creative sets are disjoint. A simple set is never creative and a creative set is never simple.