Conjunto dos Números Reais: Caracterização, Construção e Ensino - Colares, Gilderléia Bezerra (2021)
In this work we studied aspects involving the set of real numbers. We highlight three important facts that characterize this set. The first shows that, by associating rational numbers with points on a straight, it is impossible to cover the entire straight with only rational numbers. The second fact deals with the existence of incommensurable segments and the third one presents that the set of rational numbers is not a complete ordered field. We also construct the set of real numbers via Dedekind cuts. Finally, we present a proposal on how to teach the set of real numbers, for the high school students.