This is to avoid mistaken theorems based on fallible intuitions of which many instances have occurred in the history of the subject. In direct proof the conclusion is established by logically combining the axioms definitions and earlier. Mathematical Induction is a proof technique that allows us to test a theorem for all natural numbers.
So our property P P is.
By the end of this course you should be fairly familiar with proofs by contradictions and should be able to embark on your journey with proofs since you will have a solid foundation of how proof by contradiction a very basic but strong proof method really works. It has only 2 steps. First and foremost the proof is an argument. Proof by mathematical induction.