Unions and Intersections

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


If A and B are sets, it is sometimes natural to wish to unite their elements into one comprehensive set. One way of describing such a comprehensive set is to require it to contain all the elements that belong to at least one of the two members of the pair {A, B}. This formulation suggests a sweeping generalization of itself; surely a similar construction should apply to arbitrary collections of sets and not just to pairs of them. What is wanted, in other words, is the following principle of set construction.


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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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