Construção dos números reais via cortes de dedekind. - CAVALCANTE, Daniel Alves (Universidade Federal do Tocantins, 2023)
This monograph has as main objective the construction of the real numbers via cuts of Dede- kind. To do so, we will discuss the characterization of the set of natural numbers N by the Peano axioms and, from the natural numbers, we will construct the set of integers Z via equivalence relation in N×N. Then, also via equivalence relation, we will construct the set of rational num- bers Q and present some of the properties of its elements. In order to reach our research goal, we will show the insufficiency of Q to measure some line segments. Then, we will construct the set of real numbers R from the Dedekind cuts and we will present the main properties of this set, especially highlighting the one that differs from Q.