1.8 Induction

Which of the following is/are correct about Ordinary Induction and Strong Induction?

Exercise 1

 Strong induction and ordinary induction are technically equivalent. 

 Ordinary induction can be seen as a special case of strong induction where some of the assumptions are not used. 

&nbsp;A strong induction proof can be turned into ordinary induction by copying the strong induction proof with the assumptions about \(P(k) \) for \(k < n \) left out.&nbsp;

&nbsp;How to turn a strong induction proof into an ordinary one? Revise the induction hypothesis to \(Q(n) ::= \forall k \le n. P(k) \).&nbsp;

When should one use Induction vs WOP?

Exercise 2

&nbsp; It is a matter of taste - proofs that work for one can be phrased to work for the other. Induction should be used whenever there is a clear base case presented. Induction should be used whenever one wants to prove that something holds for all n. WOP should be used whenever one wants to prove that something holds for all n. It is a matter of taste - proofs that work for one can be phrased to work for the other.&nbsp;