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