You are here

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.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.

To open this file please click here.

These pdf files are furnished by JSTOR.

Classroom Capsules would not be possible without the contribution of JSTOR.

JSTOR provides online access to pdf copies of 512 journals, including all three print journals of the Mathematical Association of America: The American Mathematical Monthly, College Mathematics Journal, and Mathematics Magazine. We are grateful for JSTOR's cooperation in providing the pdf pages that we are using for Classroom Capsules.

Capsule Course Topic(s):
One-Variable Calculus | Theoretical Issues
Average: 2.9 (47 votes)