Choice and Infinitesimals

  • James M. Henle
Part of the Problem Books in Mathematics book series (PBM)

Abstract

We prove here Theorem 7.10 which offers three equivalent forms of the Axiom of Choice. We then use AC to construct a system of numbers called the Hyperreal numbers (ℍℝ). This system extends ℝ as ℝ extended ℚ and ℚ extended ℤ. ℍℝ contains both infinite numbers and infinitesimals.

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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • James M. Henle
    • 1
  1. 1.Department of MathematicsSmith CollegeNorthamptonUSA

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