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 -