11.Basic reminder on induction2.Definition of recursion3Illustration with the computation of the factorialLecture 6: Recursion3.4.Illustration with Fibonacci numbers5.The quicksort algorithm6.Recursive implementation of the quicksort algorithmWhat is induction?There are some properties which you cannot prove or derive for all cases, but which can be handled sequentially. For example, if you want to prove that the following holdsn(n+1)for all n. First, you would prove a base case, i.e. this relation is true for n=1 (you can check that this is the case).Then you will prove this fact by induction, i.e. you will assume that the property is true up to n, and show that it implies that 1 + 2 + 3 + 4 +· · ·+n=2the property is true up to n+1. This proves the property by induction.
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