17 citations · 59 across the 10 of their papers we have counts for
3 papers · 1 filter
Cauchy, infinitesimals and ghosts of departed quantifiers
Jacques Bair, Piotr Blaszczyk, Robert Ely +10
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for t…
Analyzing Benardete's comment on decimal notation
Jacques Bair, Piotr Blaszczyk, Karin U. Katz +3
Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on th…
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Tiziana Bascelli, Piotr Blaszczyk, Alexandre Borovik +7
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and…