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7 - What Is the Problem?

from Part III - The Real Numbers (and the Complex Numbers)

Published online by Cambridge University Press:  16 October 2019

T. W. Körner
T. W. Körner
Affiliation:
University of Cambridge
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Summary

We show that the rationals will not support calculus. Using the intermediate value theorem, we discuss the properties required by a number system to allow us to do calculus. We state the fundamental axiom of analysis and obtain various equivalent forms of that axiom.

Keywords

completenessirrationaldecimalrealCauchy
Type
Chapter
Information
Where Do Numbers Come From? , pp. 137 - 166
Publisher: Cambridge University Press
Print publication year: 2019

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  • What Is the Problem?
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.008
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  • What Is the Problem?
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.008
Available formats
×

Save book to Google Drive

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 Google Drive.

  • What Is the Problem?
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.008
Available formats
×