TY - JOUR

T1 - Cauchy's continuum

AU - Katz, Karin U.

AU - Katz, Mikhail G.

PY - 2011/12

Y1 - 2011/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84857140393&partnerID=8YFLogxK

U2 - 10.1162/POSC_a_00047

DO - 10.1162/POSC_a_00047

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AN - SCOPUS:84857140393

SN - 1063-6145

VL - 19

SP - 426

EP - 452

JO - Perspectives on Science

JF - Perspectives on Science

IS - 4

ER -