# 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.

## Links

## Other information

- pages
- 28

### BibTeX entry

@article{Katz2010, 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.}, author = {Katz, Karin Usadi and Katz, Mikhail G.}, month = {jul}, pages = 28, title = {When is .999... less than 1?}, 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}, collections = {Unusual arithmetic} }