The Mathematical Intelligencer

, Volume 8, Issue 2, pp 41–47 | Cite as

Infinitesimals from Leibniz to Robinson time to bring them back to school

  • Victor Harnik


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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  1. 1.
    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
  2. 2.
    H. J. Keisler,Foundations of Infinitesimal Calculus, Prindle, Weber & Schmidt, Boston, 1976.MATHGoogle Scholar
  3. 3.
    I. Lakatos, “Cauchy and the Continuum”.The Mathematical Intelligencer 1 (1978), pp. 151–161.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    A. Robinson,Non-standard Analysis, North Holland Publishing Co., Amsterdam, 1974.Google Scholar
  5. 5.
    K. Sullivan, “The Teaching of Elementary Calculus Using the Nonstandard Approach”,The American Mathematical Monthly 83 (1976), pp. 371–375.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1986

Authors and Affiliations

  • Victor Harnik
    • 1
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael

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