Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 5 - Section 5.2 - Strong Induction and Well-Ordering - Exercises - Page 343: 29

Answer

Have to Point Out What is wrong with this “proof” by strong induction? --“Theorem” For every non negative integer n, 5n = 0. Basis Step: 5 · 0 = 0.

Work Step by Step

-The error is in going from the base case n = 0 to the nextcase, n = 1; -we cannot write 1 as the sum of two smaller natural numbers.
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