A construção de Cantor dos números reais e os números hiperreais

Abstract

The aim of this study is to propose a discussion and reflection on possible approaches to Real Numbers in Basic Education, through the History of Mathematics, the construction of the set of Real Numbers and an extension of the real numbers, the Hyperreal Numbers. We will show Cantor’s construction of the real numbers, where each real number is defined as an equivalence class of Cauchy sequences of rational numbers. Subsequently, the construction of hyperreal numbers is also based on the studies published by the German mathematician Abraham Robinson. In addition to the constructions mentioned above, the last chapter of this dissertation analyzes how the set of real numbers is studied in high school mathematics according to current legislation in Brazil.