We all know about mathematical induction and well-ordering principle. Both so obvious that they can be taken as axioms. But recently I read a proof of both. In the proof of the Principle of Mathematical Induction, the author (of the book I read) uses the well-ordering principle. And surprisingly, the principle of mathematical induction is also used in proving well-ordering principle. And further, the author says that both the principles are equivalent.
How can these two principles be equivalent? They are stated differently.
Also, shouldn't one of these principles be taken as an axiom? I think that Well-ordering principle is more suitable to be taken as an axiom. Isn't it? What do you think?