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Master's Dissertation
DOI
Document
Author
Full name
Reinaldo Viana da Costa
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Ribeiro, Hermano de Souza (President)
Federson, Marcia Cristina Anderson Braz
Sampaio, Joao Carlos Vieira
Santos, Ederson Moreira dos
Title in Portuguese
Dos números naturais aos números reais
Keywords in Portuguese
Axiomas de Peano
Conjuntos numéricos
Cortes de Dedekind
Números inteiros
Números naturais
Números racionais
Números reais
Abstract in Portuguese
Este trabalho apresenta a construção dos conjuntos dos números naturais, inteiros, racionais e reais, buscando contemplar uma mediação entre alunos e professores do ensino médio que possa contribuir em uma abordagem facilitadora para o processo de ensino e aprendizagem. A construção dos conjuntos numéricos é feita de modo progressivo, apresentando leis e propriedades que definem cada um deles. Os capítulos apresentam teoremas que são provados de modo que o leitor possa conseguir, efetivamente, estabelecer um elo entre a teoria matemática e suas abstrações iniciais inerentes aos estudantes em formação.
Title in English
From natural numbers to real numbers
Keywords in English
Dedekind cuts
Integer numbers
Natural numbers
Numerical sets
Peano axioms
Rational numbers
Real numbers
Abstract in English
This work presents the construction of the sets of natural, integer, rational and real numbers, aiming to contemplate a mediation between high school students and teachers that can contribute to an easy approach to the teaching and learning processes. The construction of the numerical sets is done progressively presenting laws and properties that define each one of them. The chapters present theorems that are proven so that the reader can effectively establish a link between mathematical theory and its initial abstractions inherent in the students in formation.
 
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Publishing Date
2019-08-12
 
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