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Problem 6. Find the logical error in the following proof by induction. ( You may want to take a moment an appre- ciate that the claim is extremely false). Claim: For any real number a * 0 and any integer n > 0, a" = 1. Proof: We use strong induction on n. For the base case (n - 0): a = 1, which is true for any a # 0. Now, for the inductive step: Assume a* - 1 is true for k = 0, 1, 2, .. , n -2, n - 1, n. In particular, we see that a= an - - 1. Then a"- -20 -(1-1) 1 where the last equality holds because of the inductive hypothesis that a" - a" - - 1. So, by (strong) induction, we have shown that a" = 1