When is .999... less than 1?

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

2010-07-18

arxiv.org/abs/1007.3018v1

Montana Mathematics Enthusiast 7 (2010), 3--30

Mathematics

History and Overview

28 pages

Scientific paper

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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