Infinite Limit of Sequences and Its Phenomenology
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Mónica Arnal-Palacián 1 * , Javier Claros-Mellado 2, María Teresa Sánchez-Compaña 3
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1 University of Zaragoza, SPAIN2 Complutense University of Madrid, SPAIN3 University of Malaga, SPAIN* Corresponding Author

Abstract

In this document, we search for and define an infinite limit of sequences that is correct and accepted by the mathematical experts, the final purpose of which is to analyze its phenomenology, in Freudenthal’s sense. To make the choice, experts were consulted on two issues. The first one was not decisive because of the effect that the divergence term causes, and for this reason, we did a second expert consultation where this term was removed and we selected the definition we have analyzed in this document. Once the definition was chosen, two approaches were considered for analysis: the intuitive approach and the formal approach. Based on these two approaches, we specify certain phenomena organized by the definition: unlimited intuitive growth and unlimited intuitive decrease (intuitive approach) and one way and return infinite limit of sequences (formal approach), and show examples of such phenomena by graphical, verbal and tabular representation systems. All this aim to be a help to overcome the difficulties that pre-university students have with the concept of limit.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 15, Issue 3, October 2020, Article No: em0593

https://doi.org/10.29333/iejme/8279

Publication date: 17 May 2020

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