First Properties of ℝ

  • Sterling K. Berberian
Part of the Undergraduate Texts in Mathematics book series (UTM)


Chapter 1 lays the foundation; what are we building? Our most ambitious objective is to give a logically rigorous presentation of Calculus, learning as much as possible along the way. Everything has to come from the axioms for the field of real numbers ℝ (that in fact it does seems a miracle!). The properties of ℝ developed in this chapter lie very close to the axioms; they require some ingenuity but no essential new concepts (such as limits).


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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Sterling K. Berberian
    • 1
  1. 1.Department of MathematicsThe University of Texas at AustinAustinUSA

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