Real Numbers

  • Andrew Browder
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter, we describe the system of real numbers, deducing some of their essential properties from the axioms for a complete ordered field. Before doing so, we take a quick look at the ideas and notations of sets, relations, and functions, sketch the construction of the integers and the rational numbers (starting from the natural numbers), and indicate the need for a field larger than the rational numbers. At the end of the chapter, we sketch the proof of the existence and (essential) uniqueness of a complete ordered field.


Equivalence Class Natural Number Rational Number Order Relation Nonempty Subset 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Andrew Browder
    • 1
  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

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