A Topological Definition of Limits for Use in Elementary Calculus

We describe a topological definition of the limit that can be used as an alternative to the standard definition in elementary calculus. In particular, we replace intervals centered about the relevant quantities being approached in the domains and ranges of functions with arbitrarily small general op...

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Bibliographic Details
Published inThe College mathematics journal Vol. 45; no. 4; pp. 313 - 315
Main Authors Cooper, Charles L., McClendon, Michael S.
Format Journal Article
LanguageEnglish
Published Washington Taylor & Francis 01.09.2014
Mathematical Association of America
Taylor & Francis Ltd
Subjects
Algebra
Algebraic topology
Calculus
CLASSROOM CAPSULES
Classroom techniques
College mathematics
Educational equipment
Mathematical intervals
Open intervals
Topological manifolds
Topology
Universal algebra
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Summary:We describe a topological definition of the limit that can be used as an alternative to the standard definition in elementary calculus. In particular, we replace intervals centered about the relevant quantities being approached in the domains and ranges of functions with arbitrarily small general open intervals about those quantities. In many cases, this simplifies the work of verifying specific limits and the verification of many of the basic limit properties.
ISSN:0746-8342
1931-1346
DOI:10.4169/college.math.j.45.4.313