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Book Chapter
The Meaning of Infinity in Calculus and Computer Algebra Systems
Book Series
Lecture Notes in Computer Science
Publisher
Springer Berlin / Heidelberg
ISSN
0302-9743 (Print) 1611-3349 (Online)
Volume
Volume 2385/2002
Book
Artificial Intelligence, Automated Reasoning, and Symbolic Computation
DOI
10.1007/3-540-45470-5
Copyright
2002
ISBN
978-3-540-43865-6
DOI
10.1007/3-540-45470-5_23
Pages
165-189
Subject Collection
Computer Science
SpringerLink Date
Tuesday, January 01, 2002
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The Meaning of Infinity in Calculus and Computer Algebra Systems
Michael Beeson
6
and Freek Wiedijk
7
(6)
San José State University, USA
(7)
University of Nijmegen, The Netherlands
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.
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