Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-22T18:41:36.298Z Has data issue: false hasContentIssue false

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] 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.

  • 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 Dropbox

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 Dropbox.

  • 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
×