2012/08/05 by Pete L. Clark, Clark, Pete L.
Mathematics · #06A05 #FOS: Mathematics #History and Overview (math.HO) #math.HO #msc:06A05
paper · pdf · doi:10.48550/arxiv.1208.0973
10 pages
arxiv created 2012/08/05 · arxiv updated 2012/08/07
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.