Real Analysis in Reverse

• Published in 2012
• Added on 2021-06-07

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.

Links

• http://arxiv.org/abs/1204.4483v4
• http://arxiv.org/pdf/1204.4483v4

Other information

BibTeX entry

@article{RealAnalysisinReverse,
	key = {RealAnalysisinReverse},
	type = {article},
	title = {Real Analysis in Reverse},
	author = {James Propp},
	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.},
	comment = {},
	date_added = {2021-06-07},
	date_published = {2012-10-09},
	urls = {http://arxiv.org/abs/1204.4483v4,http://arxiv.org/pdf/1204.4483v4},
	collections = {about-proof,attention-grabbing-titles,the-act-of-doing-maths},
	url = {http://arxiv.org/abs/1204.4483v4 http://arxiv.org/pdf/1204.4483v4},
	year = 2012,
	urldate = {2021-06-07},
	archivePrefix = {arXiv},
	eprint = {1204.4483},
	primaryClass = {math.HO}
}