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Cauchy's Continuum
Article
Aug 2011
Karin U. Katz
Mikhail G. Katz
Cauchy’s sum theorem of 1821 has been the subject of rival interpretations ever since Robinson proposed a novel reading in the 1960s. Some claim that Cauchy modified the hypothesis of his theorem in 1853 by introducing uniform convergence, whose traditional formulation requires a pair of independent variables. Meanwhile, Cauchy’s hypothesis is form...
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When is .999... less than 1?
Article
Jul 2010
Karin Usadi Katz
Mikhail G. Katz
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 interpreta...
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