Uma apresentação da construção dos números reais usando sequência de Cauchy para os professores do Ensino Básico.

Abstract

In this work we will make the formal construction of real numbers using equivalence classes of Cauchy sequences of rational numbers. This construction aims to serve elementary and high school teachers, presenting a presentation with notations that facilitate understanding, unlike other presentations that present a very simplified notation, but that make it difficult for the reader to have a solid understanding of the subject. We also did a study of how this topic is treated in Basic Education, through the analysis of textbooks and internet sites (which is currently one of the main sources of research for students and teachers). We also researched the skills of the Base Nacional Comum Curricular (BNCC) linked to the real ones. We present the rational numbers and their deficiencies, which justifies the need for the completeness of this set through irrational numbers. As I already have an understanding of finite or infinite and periodic decimal expressions, as they represent numbers that can be put in the form of a fraction with an integer numerator and denominator (denominator other than zero), in this work we will also give meaning to infinite and non-repeating decimal expressions o which will expand the understanding of number beyond the set of rational numbers.