Arbitrarily Close

• Published in 2019
• Added on 2022-10-08

Mathematicians tend to use the phrase "arbitrarily close" to mean something along the lines of "every neighborhood of a point intersects a set". Taking the latter statement as a technical definition for arbitrarily close leads to an alternative development of classic concepts in real analysis such as supremum, closure, convergence and limits of sequences, closure, connectedness, compactness, and continuity. The goal of this text is to provide readers with an introduction to real analysis by taking deliberate steps to parse these difficult concepts using arbitrarily close as the kernel.

Links

• http://arxiv.org/abs/1912.13159v2
• http://arxiv.org/pdf/1912.13159v2

Other information

BibTeX entry

@book{ArbitrarilyClose,
	key = {ArbitrarilyClose},
	type = {book},
	title = {Arbitrarily Close},
	author = {John A. Rock},
	abstract = {Mathematicians tend to use the phrase "arbitrarily close" to mean something
along the lines of "every neighborhood of a point intersects a set". Taking the
latter statement as a technical definition for arbitrarily close leads to an
alternative development of classic concepts in real analysis such as supremum,
closure, convergence and limits of sequences, closure, connectedness,
compactness, and continuity. The goal of this text is to provide readers with
an introduction to real analysis by taking deliberate steps to parse these
difficult concepts using arbitrarily close as the kernel.},
	comment = {},
	date_added = {2022-10-08},
	date_published = {2019-12-07},
	urls = {http://arxiv.org/abs/1912.13159v2,http://arxiv.org/pdf/1912.13159v2},
	collections = {the-act-of-doing-maths},
	url = {http://arxiv.org/abs/1912.13159v2 http://arxiv.org/pdf/1912.13159v2},
	year = 2019,
	urldate = {2022-10-08},
	archivePrefix = {arXiv},
	eprint = {1912.13159},
	primaryClass = {math.HO}
}