The Axiom of Choice

  • John Stillwell
Chapter
First Online:
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The ZF axioms allow us to assert the existence of any set whose members are selected according to some definable “rule”—this is essentially what the replacement schema says. However, we often want to assert the existence of a set without knowing a rule for selecting its members. Typically, the members are simply “chosen” from other sets, but not according to any “rule.” When infinitely many choices are required, we may not be able to guarantee the existence of the set without some axiom of choice.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsUniversity of San FranciscoSan FranciscoUSA

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