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arXiv:1204.4483math.HO

Real Analysis in Reverse

James Propp

Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.

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.

arXiv comments
To appear in the May 2013 issue of the American Mathematical Monthly
Journal reference
DOI
Subjects
math.HOHistory and Overview

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Linked by 1 identifiable commenter in 1 comment across 1 thread, from Aug 2019 to Aug 2019.

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  1. Calculus Is Deeply Irrational 1 comment

    • Propp himself (the author) wrote a paper in 2012 called Real Analysis In Reverse, which he links to in the post but doesn't really call attention to. It's a lovely paper, and it talks about precisely what properties of the reals are enough to tell you that you really are dealing…

      Smaug123View on HNParent context

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