Cauchy's continuum

Karin U. Katz, Mikhail G. Katz

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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 formulated in terms of a single variable x, rather than a pair of variables, and requires the error term rn = rn(x) to go to zero at all values of x, including the infinitesimal value generated by 1/n, explicitly specified by Cauchy. If one wishes to understand Cauchy's modification/clarification of the hypothesis of the sum theorem in 1853, one has to jettison the automatic translation-to-limits.

Original languageEnglish
Pages (from-to)426-452
Number of pages27
JournalPerspectives on Science
Issue number4
StatePublished - Dec 2011


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