functions and sets can often be proved by an induction principle that follows the recursive definition. For example, the definition of the natural numbers presented here directly implies the principle of mathematical induction for natural numbers: if a property holds of the natural number 0 (or 1), and the property holds of whenever it holds of , then the property holds of all natural numbers (Aczel 1977:742).

Form of recursive definitions

Most recursive definitions have two foundations: a base case (basis) and an inductive

1.Previous
3.Next