As Keisler showed us, the infinitesimal, that good old heuristic tool, can be used in teaching calculus with a very slight departure from the original spirit of Leibniz. The main difference is in the explicit distinction between ≈ and = and the use of notions such as “standard part” which were not explicitly clarified before. At the classroom level, the main importance of Robinson’s contribution is that it reassures us, the teachers, that when we say “infinitesimal”, we can finally claim that we know what we are talking about.
Standard Part Integral Calculus Standard Real Infinitesimal Calculus Bright Nucleus
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H. J. Keisler,Elementary Calculus, Prindle, Weber & Schmidt, Boston, 1976. (Review: M. Davis and M. Hausner, “The Joy of Infinitesimals,”The Mathematical Intelligencer 1 (1978), pp. 168-170).MATHGoogle Scholar
H. J. Keisler,Foundations of Infinitesimal Calculus, Prindle, Weber & Schmidt, Boston, 1976.MATHGoogle Scholar