Interesting Esoterica

Real Analysis in Reverse

Article by James Propp
  • Published in 2012
  • Added on
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.

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BibTeX entry

@article{RealAnalysisinReverse,
	title = {Real Analysis in Reverse},
	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.},
	url = {http://arxiv.org/abs/1204.4483v4 http://arxiv.org/pdf/1204.4483v4},
	year = 2012,
	author = {James Propp},
	comment = {},
	urldate = {2021-06-07},
	archivePrefix = {arXiv},
	eprint = {1204.4483},
	primaryClass = {math.HO},
	collections = {about-proof,attention-grabbing-titles,the-act-of-doing-maths}
}