TY - JOUR

T1 - Fermat, Leibniz, Euler, and the gang

T2 - The true history of the concepts of limit and shadow

AU - Bascelli, Tiziana

AU - Bottazzi, Emanuele

AU - Herzberg, Frederik

AU - Kanovei, Vladimir

AU - Katz, Karin U.

AU - Katz, Mikhail G.

AU - Nowik, Tahl

AU - Sherry, David

AU - Shnider, Steven

N1 - cited By 25

PY - 2014/9

Y1 - 2014/9

N2 - Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.

AB - Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.

UR - http://www.scopus.com/inward/record.url?scp=84901435271&partnerID=8YFLogxK

U2 - 10.1090/noti1149

DO - 10.1090/noti1149

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SN - 0002-9920

VL - 61

SP - 848

EP - 864

JO - Notices of the American Mathematical Society

JF - Notices of the American Mathematical Society

IS - 8

ER -