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

@article{Katz2010WhenI, title={When is .999... less than 1?}, author={Karin U. Katz and Mikhail G. Katz}, journal={The Mathematics Enthusiast}, year={2010} }

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…

## 27 Citations

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The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity, is discussed via a proceptual analysis of the meaning of the ellipsis “...” in the real formula.

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The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity, is discussed via a proceptual analysis of the meaning of the ellipsis “...” in the real formula.

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