# When is .999... less than 1?

- Published in 2010
- Added on

In the collection

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.

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## Other information

- key
- Katz2010
- type
- article
- date_added
- 2015-11-19
- date_published
- 2010-07-01
- pages
- 28

### 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} }