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Sets

  • Ray Mines
  • Fred Richman
  • Wim Ruitenburg
Part of the Universitext book series (UTX)

Abstract

The classical view of mathematics is essentially descriptive: we try to describe the facts about a static mathematical universe. Thus, for example, we report that every polynomial of odd degree has a root, and that there is a digit that occurs infinitely often in the decimal expansion of π. In opposition to this is the constructive view of mathematics, which focuses attention on the dynamic interaction of the individual with the mathematical universe; in the words of Hao Wang, it is a mathematics of doing, rather than a mathematics of being. The constructive mathematician must show how to construct a root of a polynomial of odd degree, and how to find a digit that occurs infinitely often in the decimal expansion of π.

Keywords

Categorical Product Binary Sequence Maximal Chain Modular Lattice Constructive Proof 
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 1988

Authors and Affiliations

  • Ray Mines
    • 1
  • Fred Richman
    • 1
  • Wim Ruitenburg
    • 2
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of Mathematics, Statistics, and Computer ScienceMarquette UniversityMilwaukeeUSA

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