The Meaning of Infinity in Calculus and Computer Algebra Systems

  • Michael Beeson
  • Freek Wiedijk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2385)


We use filters of open sets to provide a semantics justifying the use of infinity in informal limit calculations in calculus, and in the same kind of calculations in computer algebra. We compare the behavior of these filters to the way Mathematica behaves when calculating with infinity.

We stress the need to have a proper semantics for computer algebra expressions, especially if one wants to use results and methods from computer algebra in theorem provers. The computer algebra method under discussion in this paper is the use of rewrite rules to evaluate limits involving infinity.


Topological Space Theorem Prover Computer Algebra Computer Algebra System Nonstandard Analysis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael Beeson
    • 1
  • Freek Wiedijk
    • 2
  1. 1.San José State UniversityUSA
  2. 2.University of NijmegenThe Netherlands

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