Real Analysis in Reverse

2012/04/19 by James Propp, Propp, James · 2 citations
Mathematics · #12J15 #97F50 #97I99 #FOS: Mathematics #History and Overview (math.HO) #math.HO #msc:12J15 #msc:97F50 #msc:97I99

paper · pdf · doi:10.48550/arxiv.1204.4483

To appear in the May 2013 issue of the American Mathematical Monthly

arxiv created 2013/02/06 · arxiv updated 2013/02/07

Abstract

Many of the theorems of real analysis, against the background of the ordered field axioms, are equivalent to Dedekind completeness, and hence can serve as completeness axioms for the reals. In the course of demonstrating this, the article offers a tour of some less-familiar ordered fields, provides some of the relevant history, and considers pedagogical implications.

Cited by

• On the (in)equivalence of Brouwer's fixed point theorem and Sperner's lemma
• L'Hôpital's Rule is Equivalent to the Least Upper Bound Property

Related

• Another Proof of the Existence a Dedekind Complete Totally Ordered Field
• Completeness of Ordered Fields
• Axioms for the Real Numbers: A Constructive Approach
• The grounding for Continuum
• The Instructor's Guide to Real Induction