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10 - A Plethora of Polynomials

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 use our results on complex numbers to show that every polynomial has a root. We show that there exist real numbers which are not the root of a polynomial with rational coefficients. We produce a number system which is too big to be used for ordinary analysis (more precisely, a non-Archimedean ordered field).

Keywords

polynomialrootLiouvilletranscendentalnon-Archimedean
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Chapter
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Where Do Numbers Come From? , pp. 199 - 220
Publisher: Cambridge University Press
Print publication year: 2019

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  • A Plethora of Polynomials
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.011
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  • A Plethora of Polynomials
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.011
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.

  • A Plethora of Polynomials
  • T. W. Körner, University of Cambridge
  • Book: Where Do Numbers Come From?
  • Online publication: 16 October 2019
  • Chapter DOI: https://doi.org/10.1017/9781108768863.011
Available formats
×