Well-ordering priciple

The well-ordering principle is a concept, which is equivalent to mathematical induction. The theorem stated that every non-empty subset of the natural numbers has a least element.

Proof: Let A be a non-empty subset of N. We wish to show that A has a least element, that is, that there is an element a∈A such that a is greater or equal to n for n∈A.

                            P(n) : “If n ∈ A, then A has a least element.

Basic Step: P(0) is clearly true, since 0 ≤ n for all n ∈ N.