Recursive Set - Examples

Examples

  • Every finite or cofinite subset of the natural numbers is computable. This includes these special cases:
    • The empty set is computable.
    • The entire set of natural numbers is computable.
    • Each natural number (as defined in standard set theory) is computable; that is, the set of natural numbers less than a given natural number is computable.
  • The set of prime numbers is computable.
  • A recursive language is a recursive subset of a formal language.
  • The set of Gödel numbers of arithmetic proofs described in Kurt Gödel's paper "On formally undecidable propositions of Principia Mathematica and related systems I"; see Gödel's incompleteness theorems.

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