A construção ortodoxa dos números : dos números naturais aos complexos

• Ano de defesa: 2017
• Autor(a) principal: Oliveira, Wesley Sidney Santos
• Orientador(a): Araujo, Gerson Cruz
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Sergipe
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• País: Brasil
• Palavras-chave em Português: Matemática; Axiomas; Números reais; Números complexos; Axiomas de Peano
• Palavras-chave em Inglês: Peano axioms; Real numbers; Complex numbers
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://ri.ufs.br/handle/riufs/6522

In this work, we investigated the construction of natural, integer, rational, real, complex, quaternion and Octonion numbers. More precisely, the set of real numbers was achieved by applying two methods: Dedekind Cuts and Equivalence Classes of Cauchy Sequences. Our study is only based on using Peano Axioms, which are directly related to the natural numbers, in order to get the basic properties satis ed by these numbers. In addition, we carefully proved the elementary results involving real numbers. This process in question was developed constructively throughout of the concepts of the integer and rational numbers. Next, we show that it is possible to establish the existence of complex numbers along with their more usual arithmetic properties. Finally, we nish each chapter of our work showing some possible applications in each set worked.