Mathematical Induction

  • Daniel W. Cunningham
Chapter

Abstract

Proof by mathematical induction is a special method of proof that is often used to establish that certain statements are true for every natural number. We shall first discuss the well-ordering principle and a proof strategy that is used to prove that every natural number n>1 is divisible by a prime number. An explicit proof strategy is presented that will be used in proofs by mathematical induction. After reviewing the basic properties of sequences and summation notation, we carefully show the reader how to correctly use the induction proof strategy. The final sections focus on recursive definitions and proof by strong induction. The chapter ends with a proof of the fundamental theorem of arithmetic.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel W. Cunningham
    • 1
  1. 1.Mathematics DepartmentBuffalo State CollegeBuffaloUSA

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