Some historical issues and paradoxes regarding the concept of infinity: An APOS analysis: Part 2

被引：2

作者：

Dubinsky E. ^{[1
]}

Weller K. ^{[2
]}

McDonald M.A. ^{[3
]}

Brown A. ^{[4
]}

机构：

[1] Department of Mathematics, Kent State University, Kent

[2] Department of Mathematics, University of North Texas, Denton

[3] Department of Mathematics, Occidental College, Los Angeles

[4] Department of Mathematical Sciences, Indiana University South Bend, South Bend

来源：

Educational Studies in Mathematics | 2005年 / 60卷 / 2期

关键词：

APOS theory; Encapsulation; History of mathematics; Human conceptions of the infinite; Infinite processes; Infinitesimals; Limit; Natural numbers;

D O I：

10.1007/s10649-005-0473-0

中图分类号：

学科分类号：

摘要：

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. © Springer 2005.

引用

页码：253 / 266

页数：13

共 27 条

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