What is wrong with the following “proof" of the "fact" that n+3 = n+7 for all values of n (besides of course that the thing it is claiming to prove is false)? Proof. Let P(n) be the statement that n + 3 = n + 7. We will prove that P(n) is true for all n e N. Assume, for induction that P(k) is true. That is, k + 3 = k + 7. We must show that P(k + 1) is true. Now since k +3 = k + 7, add 1 to both sides. This gives k + 3 +1 = k + 7 + 1. %3D

What is wrong with the following “proof" of the "fact" that n+3 = n+7 for all values of n (besides of course that the thing it is claiming to prove is false)? Proof. Let P(n) be the statement that n + 3 = n + 7. We will prove that P(n) is true for all n e N. Assume, for induction that P(k) is true. That is, k + 3 = k + 7. We must show that P(k + 1) is true. Now since k +3 = k + 7, add 1 to both sides. This gives k + 3 +1 = k + 7 + 1. %3D

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.5: Mathematical Induction

Problem 42E

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