The Cantor–Schröder–Bernstein Theorem

  • Ulrich Daepp
  • Pamela Gorkin
Part of the Undergraduate Texts in Mathematics book series (UTM)


Suppose we have two finite sets. We have developed enough machinery to tell when one set has more elements than another. But what about infinite sets? For example, we might consider \(\mathbb{N}\) and \(\mathbb{Z^+}\), and we may ask which one has more elements. Well, we have already developed mathematical concepts that convince us that these two sets have the same number of elements. In this chapter, we investigate the situation for general infinite sets.


Partial Order Injective Function Cardinal Number Continuum Hypothesis Bernstein Theorem 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsBucknell UniversityLewisburgUSA

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