Paradoxes in Mathematics

  • Peter Hilton
  • Derek Holton
  • Jean Pedersen
Part of the Undergraduate Texts in Mathematics book series (UTM)


A good dictionary will give two (or perhaps more) distinct meanings of the word “paradox.” The first meaning is “a self-contradictory statement”; thus the celebrated classical paradox due to Bertrand Russell (1872–1970), based on a naive set theory which permits the proposition x ∈ x. A popular, but not very accurate, form of this paradox is contained in the following little story:

In the little village of Humblemeir there is a male barber. Now this barber shaves only those men who don’t shave themselves. When you think about it, this leads to a paradox. Who shaves the barber? If he shaves himself, he doesn’t, because he only shaves those who don’t shave themselves. On the other hand, if he doesn’t shave himself, he does, because he only shaves those who don’t shave themselves.


Tennis Player Baseball Player Entire Season Batting Average Comparative Adjective 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Peter Hilton
    • 1
  • Derek Holton
    • 2
  • Jean Pedersen
    • 3
  1. 1.Mathematical Sciences DepartmentSUNY at BinghamtonBinghamtonUSA
  2. 2.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  3. 3.Department of Mathematics and Computer ScienceSanta Clara UniversitySanta ClaraUSA

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