English

Real Analysis in Reverse

History and Overview 2013-02-07 v4

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.

Keywords

Cite

@article{arxiv.1204.4483,
  title  = {Real Analysis in Reverse},
  author = {James Propp},
  journal= {arXiv preprint arXiv:1204.4483},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-21T20:52:20.540Z