Paradoxes and Sophisms in Calculus

Sergiy Klymchuk; Susan Staples

doi:10.5948/9781614441106

Paradoxes and Sophisms in Calculus offers a delightful supplementary resource to enhance the study of single variable calculus. By the word paradox the authors mean a surprising, unexpected, counter-intuitive statement that looks invalid, but in fact is true. The word sophism describes intentionally invalid reasoning that looks formally correct, but contains a subtle mistake or flaw. In other words, a sophism is a false proof of an incorrect statement. A collection of over fifty paradoxes and sophisms showcases the subtleties of this subject and leads students to contemplate the underlying concepts. A number of the examples treat historically significant issues that arose in the development of calculus, while others more naturally challenge readers to understand common misconceptions. Sophisms and paradoxes from the areas of functions, limits, derivatives, integrals, sequences, and series are explored. Solutions for each paradox and explanations of the fallacious reasoning in each sophism are provided in later sections. This book serves as a complementary companion to the first authors previous book Counterexamples in Calculus (MAA), recipient of the 2010 Outstanding Academic Title Award from Choice Magazine of the American Library Association.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Paradoxes and Sophisms in Calculus

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-vi

Dedication
pp vii-viii

Contents
pp ix-xiv

Introduction
pp 1-4

Acknowledgments
pp 5-6

I - Paradoxes
pp 7-8

1 - Functions and Limits
pp 9-16

2 - Derivatives and Integrals
pp 17-20

II - Sophisms
pp 21-22

3 - Functions and Limits
pp 23-38

4 - Derivatives and Integrals
pp 39-46

III - Solutions to Paradoxes
pp 47-48

5 - Functions and Limits
pp 49-62

6 - Derivatives and Integrals
pp 63-72

IV - Solutions to Sophisms
pp 73-74

7 - Functions and Limits
pp 75-88

8 - Derivatives and Integrals
pp 89-94

Bibliography
pp 95-96

About the Authors
pp 97-98

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

Paradoxes and Sophisms in Calculus

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information