Ordinal Numbers

  • Paul R. Halmos
Part of the Undergraduate Texts in Mathematics book series (UTM)


The successor x + of a set x was defined as x ⋃ {x}, and then ω was constructed as the smallest set that contains 0 and that contains x + whenever it contains x. What happens if we start with ω, form its successor ω +, then form the successor of that, and proceed so on ad infinitum? In other words: is there something out beyond ω, ω +, (ω +)+, ⋯, etc., in the same sense in which ω is beyond 0, 1, 2, ⋯, etc.?


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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsSanta Clara UniversitySanta ClaraUSA

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