When is .999... less than 1?

• Published in 2010
• Added on 2015-11-19

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999 . . . be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.

Links

• http://arxiv.org/abs/1007.3018
• http://arxiv.org/pdf/1007.3018v1

Other information

BibTeX entry

@article{Katz2010,
	key = {Katz2010},
	type = {article},
	title = {When is .999... less than 1?},
	author = {Katz, Karin Usadi and Katz, Mikhail G.},
	abstract = {We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999 . . . be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.},
	comment = {},
	date_added = {2015-11-19},
	date_published = {2010-07-01},
	urls = {http://arxiv.org/abs/1007.3018,http://arxiv.org/pdf/1007.3018v1},
	collections = {Unusual arithmetic},
	month = {jul},
	pages = 28,
	url = {http://arxiv.org/abs/1007.3018 http://arxiv.org/pdf/1007.3018v1},
	year = 2010,
	archivePrefix = {arXiv},
	eprint = {1007.3018},
	primaryClass = {math.HO},
	urldate = {2015-11-19}
}