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.
Résumé
Cet article se penche sur certains traits spécifiques qui entrent en jeu lorsqu’il s’agit d’accorder une place à l’infini tel qu’il apparaît dans la théorie des ensembles. L’article est centré sur les conceptions de deux personnes hautement qualifiées dans le domaine des mathématiques, telles que ces conceptions se manifestent dans les variations apportées à un paradoxe bien connu: celui des balles de ping-pong. La thèorie APOS est utilisèe comme cadre pour interprèter les efforts des participants lorsqu’ils tentent de rèsoudre les paradoxes. Les cas analysès sont centrès sur les façons dont la soustraction transfinie peut être conceptualisèe, et suggèrent que le concept d’infini réel implique plus qu’une simple capacité ‘d’agir’ sur un objet complété: la manière dont se produit l’action sur les objets serait également significative.
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Mamolo, A. How to Act? A Question of Encapsulating Infinity. Can J Sci Math Techn 14, 1–22 (2014). https://doi.org/10.1080/14926156.2014.874613
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DOI: https://doi.org/10.1080/14926156.2014.874613