Question

This is more of a theoritical question: So, sometimes with induction instead of proving the induction step (so n -> n+1) its handier to prove the contrapositive of it. However, in cases where this happens not only (not (n+1) -> not n) is being proved, but also (not n -> not (n-1) ) etc until you prove the contrapositive of the base case (it's called infinite descent). My question is, why do you have to use infinite descent when proving the contrapositive and can't you just prove that not (n+1) -> not n? Where is that stated in the definition of induction? Thanks in advance!

Answer 1