English

When is .999... less than 1?

History and Overview 2010-07-20 v1

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.

Cite

@article{arxiv.1007.3018,
  title  = {When is .999... less than 1?},
  author = {Karin Usadi Katz and Mikhail G. Katz},
  journal= {arXiv preprint arXiv:1007.3018},
  year   = {2010}
}

Comments

28 pages

R2 v1 2026-06-21T15:49:30.315Z