Abstract

VILLABONA MILLAN, Diana Paola  and  ROA FUENTES, Solange. Infinite iterative processes and transcendent objects: A model of construction of mathematical infinity from the APOS Theory. Educ. mat. [online]. 2016, vol.28, n.2, pp.119-150.  Epub Apr 08, 2022. ISSN 2448-8089.  https://doi.org/10.24844/em2802.05.

The present study aims to examine the mental structures that a person can develop to construct the mathematical concept of infinity in two particular contexts: "the paradox of Achilles and the tortoise" and the "Sierpiński triangle". Based on the genetic generic decomposition of the infinite, proposed by Roa-Fuentes and Oktaç (2014), this investigation focuses on the study of the particular characteristics, mechanisms and structures produced by each context. The analysis of data from work done by postgraduate students (in Mathematics and Mathematics Education) shows how from the infinite iterative process (potential infinity) advances towards to a transcend object (actual infinity). Furthermore, the results reflect the importance of the coordination mechanism in the construction of infinite iterative process.

Keywords : APOS theory; paradoxes; Sierpiński triangle, infinite iterative processes; transcendent objects.

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