Abstract

This article investigates some of the specific features involved in accommodating the idea of actual infinity as it appears in set theory. It focuses on the conceptions of two individuals with sophisticated mathematics background, as manifested in their engagement with variations of a well-known paradox: the ping-pong ball conundrum. The APOS theory is used as a framework to interpret participants' efforts to resolve the paradoxes. The cases discussed focus on how transfinite subtraction may be conceptualized, and they suggest that there is more to accommodating the idea of actual infinity than the ability to act on a completed object--rather, it is the manner in which objects are acted upon that is also significant.

Citation

Mamolo, A. (2014). How to Act? a Question of Encapsulating Infinity. Canadian Journal of Science, Mathematics and Technology Education, 14(1), 1-22. Retrieved March 23, 2023 from https://www.learntechlib.org/p/168021/.

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Keywords

• College Faculty
• College Students
• Foreign Countries
• learning theories
• Logical Thinking
• Mathematical Aptitude
• Mathematical Concepts
• PRIOR LEARNING
• student attitudes
• Subtraction
• Theories