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Why We Don't Do Calculus on the Rational Numbers

by Scott E. Brodie (Mount Sinai School of Medicine, NY)

This article originally appeared in:
College Mathematics Journal
March, 1999

Subject classification(s): Calculus | Advanced Calculus
Applicable Course(s): 3.1 Mainstream Calculus I | 4.11 Advanced Calc I, II, & Real Analysis

The author shows that The Intermediate Value Theorem, The Maximum Value Theorem, and The Mean Value Theorem all fail for functions continuous on the rationals.


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Capsule Course Topic(s):
One-Variable Calculus | Theoretical Issues
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