Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T07:53:09.158Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo-ordered fields

Published online by Cambridge University Press:  03 November 2016

Peter Csontos ,
Christopher L. Morgan  and
Kenneth Rebman
Peter Csontos
Affiliation:
California State University, Hayward, California 94542, USA
Christopher L. Morgan
Affiliation:
California State University, Hayward, California 94542, USA
Kenneth Rebman
Affiliation:
California State University, Hayward, California 94542, USA
Get access Rights & Permissions [Opens in a new window]

Extract

A danger in teaching familiar material is oversimplification. In this article, we shall explore an example of this.

One of the authors observed a colleague (at another institution) introduce his students to the ordering of the real numbers by stating that < is a relation on ℝ which satisfies the following axiom system:

“For all x, y, z in ℝ:

  1. 1. Exactly one of x = y, x < y, y < x holds.

  2. 2. If x < y and 0 < z, then xz < yz.

  3. 3. If x < y, then x + z < y + z.”

Type
Research Article
Information
The Mathematical Gazette , Volume 58 , Issue 405 , October 1974 , pp. 195 - 198
Copyright
Copyright © Mathematical Association 1974

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.)

References

1. Niven, I. and Zuckerman, H. S., An introduction to the theory of numbers (2nd edn.). Wiley (New York, 1966).Google Scholar
2. Dickson, L. E., Linear groups (with an exposition of the Galois field theory). Dover (1958).Google Scholar