The Completeness of IR. Uncountable Sets

  • Edwin E. Moise
Part of the Universitext book series (UTX)


We now approach the proof that ℝ is uncountable. Since the set Q of all rational numbers is countable, it is clear that any valid proof of the uncountability of ℝ must use the continuity of ℝ. The classical formulation of this is as follows.

Copyright information

© Springer-Verlag New York, Inc. 1982

Authors and Affiliations

  • Edwin E. Moise
    • 1
  1. 1.Department of Mathematics Queens CollegeCity University of New YorkFlushingUSA

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