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… 
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