Conjunto dos Números Reais: Caracterização, Construção e Ensino

In this work we studied aspects involving the set of real numbers. We highlight three important facts that characterize this set. The first shows that, by associating rational numbers with points on a straight, it is impossible to cover the entire straight with only rational numbers. The second fact...

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Detalhes bibliográficos
Autor: Colares, Gilderléia Bezerra
Tipo de documento: dissertação
Estado:Versão publicada
Data de publicação:2021
País:Brasil
Recursos:Universidade Estadual do Oeste do Paraná (UNIOESTE)
Repositório:Biblioteca Digital de Teses e Dissertações do UNIOESTE
Idioma:português
OAI Identifier:oai:tede.unioeste.br:tede/5749
Acesso em linha:http://tede.unioeste.br/handle/tede/5749
Access Level:Acceso aberto
Palavra-chave:Números Reais
Cortes de Dedekind
Segmentos Incomensuráveis
Corpo Ordenado Completo
Real Numbers
Dedekind Cuts
Incommensurable Segments
Complete Ordered Field
Ensino de Matemática
Descrição
Resumo:In this work we studied aspects involving the set of real numbers. We highlight three important facts that characterize this set. The first shows that, by associating rational numbers with points on a straight, it is impossible to cover the entire straight with only rational numbers. The second fact deals with the existence of incommensurable segments and the third one presents that the set of rational numbers is not a complete ordered field. We also construct the set of real numbers via Dedekind cuts. Finally, we present a proposal on how to teach the set of real numbers, for the high school students.