The Theoretical didactic approach to the counterexample in mathematics

Abstract

This article describes a theoretical-didactic approach to the counterexample within mathematics and its process of teaching-learning, emphasizing the importance of inducing a logical thinking by introducing counterexamples as a process of maturation of mathematical thinking. In addition, it is argued that the counterexamples are not very used in the teaching of mathematics, unlike the important role they have in the professional mathematic activity.