GeoGebra as a Potential Tool for Exploring the Concepts of Continuity and Convergence GeoGebra como una Herramienta Potencial para Explorar los Conceptos de Continuidad y Convergencia

Abstract

This paper exemplifies the potential of GeoGebra as a didactic resource for teaching Real and Complex Analysis. To be more precise, our main goal is to demonstrate how useful GeoGebra is in providing a visual approach for understanding the concepts of continuity, equicontinuity, and the convergence of sequences of real functions of two variables and complex functions of a single variable. The complexity of the definition of these concepts, which rely on various parameters such as classical delta and epsilon, motivated the choice of the subject of this article. Additionally, their connection to the Ascoli-Arzelà Theorem, which is significant in many areas of mathematics, also influenced this decision. Throughout the paper, we present some applets developed using GeoGebra which allow a satisfactory exploration of those concepts according to our analysis. This exploration is made along a sequence of examples and counterexamples for the concepts of continuity, equicontinuity, and convergence addressed. In the Appendix, we provide some instructions for designing the applets used along the text.