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Cardinal and Ordinal Arithmetic

  • Iain T. Adamson

Abstract

Let (a i )iI be a family of cardinals indexed by a set I. The cardinal sum or simply the sum ΣiI a i of (a i )iI is defined to be the cardinal of the union ∪iI(aix). If a and b are cardinals then the sum a+ b of a and b is defined to be the cardinal of (a × 0) ∪ (b × 1). Notice that in these definitions the sets forming the unions are equipotent to the cardinals being added but (thanks to their second factors) are pairwise disjoint.

Keywords

Real Number Natural Number Mathematical Logic Pairwise Disjoint Ordinal Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Iain T. Adamson
    • 1
  1. 1.Department of MathematicsThe University of DundeeDundeeScotland

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