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 -