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Ordinal Numbers

  • Gaisi Takeuti
  • Wilson M. Zaring
Part of the Graduate Texts in Mathematics book series (GTM, volume 1)

Abstract

The theory of ordinal numbers is essentially a theory of well ordered sets. For Cantor an ordinal number was “the general concept which results from (a well-ordered aggregate) M if we abstract from the nature of its elements while retaining their order of precedence ...” It was Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970), working independently, who removed Cantor’s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism.

Keywords

Minimal Element Ordinal Number Order Preserve Proper Class Order Isomorphism 
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-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Gaisi Takeuti
    • 1
  • Wilson M. Zaring
    • 1
  1. 1.University of IllinoisUSA

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