A recursive description of a set consists of three steps: ?

  • Basis step: Specify one or more elements of .
  • Recursive step: Give one or more rules to construct new elements of from existing elements of .
  • Exlusion rule: State that consists only of the elements that are specified by the basis step, or generated by successive applications of the recursive step. Nothing else is in the . (This step is usually assumed rather than explicitly stated)