Find the mistake in the following proof that purports to show that every nonnegative integer power of every nonzero real number is 1. Proof: Letr beanynonzerorealnumberandlettheproperty P(n) be the equation rn =1. Show that P(0) is true:P(0) is true becauser0 =1 by definition of zeroth power. Show that for all integers k0, if P(i) is true for all integers i from 0 through k, then P(k+1) is also true:Let k be any integer with k 0 and suppose that ri =1 for all integers i from 0 through k. This is the inductive hypothesis. We must show that rk+1 =1. Now rk+1 =rk+k(k1) becausek+k(k1) =k+kk+1=k+1 = rkrk rk1 by the laws of exponents = 11 1 by inductive hypothesis =1. Thus rk+1 =1 [as was to be shown]. [Since we have proved the basis step and the inductive step of the strong mathematical induction, we conclude that the given statement is true.]

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