The Meaning of Infinity in Calculus and Computer Algebra Systems

  • Authors:

  • Michael Beeson;Freek Wiedijk

  • Affiliations:

  • -;-

  • Venue:
  • AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
  • Year:
  • 2002

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Abstract

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.