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- Title
DEL INFINITO POTENCIAL AL ACTUAL: UN RECORRIDO HISTÓRICO A TRAVÉS DE LA METÁFORA CONCEPTUAL.
- Authors
Díaz-Chang, Tamara; Arredondo, Elizabeth-H
- Abstract
In this article we address the historical and epistemological analysis of infinity as a mathematical concept, seen through the lens of conceptual metaphors, trying to specify the obstacles that prevented, for long periods of our history, the acceptance of actual infinity, allowing only the existence of potential infinite. We argue that this kind of analysis is of special relevance to be considered in research agendas within the didactics of mathematics. In particular, we will show how the development of certain conceptual metaphors led to a process of axiomatization of actual infinity, which ended with the works of Georg Cantor. The implemented methodology is supported by a qualitative and argumentative bibliographic research based on a metaethnography. From this research, information is obtained about the mathematical structures which are been mapped between starting and ending domains of conceptual metaphors, through which mathematical infinity was developed during four main stages of history, showing the transition from potential infinity to actual infinity. In particular, at least five different metaphors are identified that the teacher must consider and the student must develop to achieve a proper understanding of mathematical infinity.
- Subjects
MATHEMATICAL analysis; INFINITY (Mathematics); CONCEPTUAL history; ETHNOLOGY; HISTORICAL analysis; MATHEMATICS; METAPHOR
- Publication
Paradigma, 2021, Vol 42, Issue 1, p106
- ISSN
1011-2251
- Publication type
Article
- DOI
10.37618/paradigma.1011-2251.2021.p106-132.id992