The Instructor’s Guide to Real Induction
Pete L. Clark · Mathematics Magazine · 2019
Summary.We introduce real induction, a proof technique analogous to Mathematical Induction but applicable to statements indexed by an interval on the real line. We apply these principles to give streamlined, conceptual proofs of basic results in elementary real analysis and topology. Then we pursue inductive principles in arbitrary ordered sets. Applications are given, e.g., to “real analysis in reverse.”