Construção do corpo dos números reais via cortes de Dedekind

• Ano de defesa: 2017
• Autor(a) principal: Xavier, Valmir Heráclito Nascimento
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Física; Programa de Pós-Graduação em Física; UFPB
• Palavras-chave em Português: Corpo dos números racionais; Cortes de Dedeking; Corpos algébricos; Feld of the ractional numbers; Feld of the real numbers; Dedekind cuts, algebraic fields; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/12804

In this work, we present the notion of Dedekind cuts motivated by the study of the polynomial equation x2 = 2 in the fields of rational numbers. We introduce the operations of addition and multiplication between cuts, as well as the notion of absolute value and order relation between cuts. We prove that the set of Dedekind cuts equippaded with the operations of addition and multiplication is an ordered field. We present the construction of the field of the real numbers by exploring the fact that the field of the Dedekind cuts are ordered and complete.