Question

Prove well-ordering principle for natural numbers using the principle of mathematical induction

Answer 1

It now follows byPrinciple of Mathematical Induction that and hence A = N − B = ∅ which is contrary to the assumption that is non-empty. It follows from this contradiction that must have a least member. It is possible to prove thePrinciple of Mathematical Induction by assuming the truth of Well Ordering Principle.