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Some Historical Issues and Paradoxes regarding the Concept of Infinity: An Apos-Based Analysis: Part 1

This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations ar...

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Published in:	Educational studies in mathematics 2005-03, Vol.58 (3), p.335-359
Main Authors:	Dubinsky, Ed, Weller, Kirk, McDonald, Michael A., Brown, Anne
Format:	Article
Language:	English
Subjects:	Analysis Cognitive Processes Encapsulation Human information processing Infinite Infinite sets Infinity Logic Logical Thinking Mathematical Concepts Mathematical functions Mathematical objects Mathematical sets Mathematics Mathematics Education Natural numbers Paradox Paradoxes Polarity Study and teaching Tennis balls Word Problems (Mathematics)
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description	This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of interiorization and encapsulation. Our purpose for providing a cognitive perspective is that issues involving the infinite have been and continue to be a source of interest, of controversy, and of student difficulty. We provide a cognitive analysis of these issues as a contribution to the discussion. In this paper, Part 1, we focus on dichotomies and paradoxes and, in Part 2, we will discuss the notion of an infinite process and certain mathematical issues related to the concept of infinity.
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ispartof	Educational studies in mathematics, 2005-03, Vol.58 (3), p.335-359
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source	JSTOR Archival Journals and Primary Sources Collection; Springer Nature; ERIC
subjects	Analysis Cognitive Processes Encapsulation Human information processing Infinite Infinite sets Infinity Logic Logical Thinking Mathematical Concepts Mathematical functions Mathematical objects Mathematical sets Mathematics Mathematics Education Natural numbers Paradox Paradoxes Polarity Study and teaching Tennis balls Word Problems (Mathematics)
title	Some Historical Issues and Paradoxes regarding the Concept of Infinity: An Apos-Based Analysis: Part 1
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