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Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An Apos Analysis: Part 2

  • Ed Dubinsky
  • Kirk Weller
  • Michael A. McDonald
  • Anne Brown
Article

Abstract

This is Part 2 of a two-part study of how APOS theory may be used to provide cognitive explanations of how students and mathematicians might think about the concept of infinity. We discuss infinite processes, describe how the mental mechanisms of interiorization and encapsulation can be used to conceive of an infinite process as a completed totality, explain the relationship between infinite processes and the objects that may result from them, and apply our analyses to certain mathematical issues related to infinity.

Key Words

APOS theory encapsulation history of mathematics human conceptions of the infinite infinite processes infinitesimals limit natural numbers 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Ed Dubinsky
    • 1
  • Kirk Weller
    • 2
  • Michael A. McDonald
    • 3
  • Anne Brown
    • 4
  1. 1.Department of MathematicsKent State UniversityKentUSA
  2. 2.Department of MathematicsUniversity of North TexasDentonUSA
  3. 3.Department of MathematicsOccidental CollegeLos AngelesUSA
  4. 4.Department of Mathematical SciencesIndiana University South BendSouth BendUSA

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