2012•arXiv (Cornell University)Open access

The Instructor's Guide to Real Induction

Pete L. Clark

Abstract

We introduce real induction, a proof technique analogous to mathematical induction but applicable to statements indexed by an interval on the real line. More generally we give an inductive principle applicable in any Dedekind complete linearly ordered set. Real and ordered induction is then applied to give streamlined, conceptual proofs of basic results in honors calculus, elementary real analysis and topology.

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Key concepts: Mathematical induction, Real line, Mathematical proof, Real analysis, Dedekind cut, Calculus (dental), Real number, Inductive method