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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2014.tde-08042015-143010
Document
Author
Full name
Bruno Andrade Borges
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2014
Supervisor
Committee
Galvez, Americo Lopez (President)
Azevedo, Katia Andreia Gonçalves de
Lamas, Rita de Cássia Pavani
Nascimento, Marcelo José Dias
Title in Portuguese
O infinito na matemática
Keywords in Portuguese
Cardinalidade
Conjuntos enumeráveis
Infinito
Infinito actual
Infinito potencial
Abstract in Portuguese
Nesta dissertação, abordaremos os dois tipos de infinitos existentes: o infinito potencial e o infinito actual. Apresentaremos algumas situações, exemplos que caracterizam cada um desses dois tipos. Focaremo-nos no infinito actual, com o qual discutiremos alguns dos desafios encontrados na teoria criada por Cantor sobre este assunto. Mostraremos também sua importância e a diferença entre este e o infinito potencial. Com isso, buscamos fazer com que o professor compreenda adequadamente os fundamentos matemáticos necessários para que trabalhe, ensine e motive apropriadamente seus alunos no momento em que o infinito e conjuntos infinitos são discutidos em aula. Desta forma, buscamos esclarecer os termos usados e equívocos comuns cometidos por alunos e também professores, muitas vezes enganados ou confundidos pelo senso comum.
Title in English
Infinity in mathematics
Keywords in English
Actual
Cardinality
Countable sets
Infinity
Potential infinity
Abstract in English
In this dissertation, we will discuss the two types of infinities: the potential infinity and the actual infinity. We will present some situations, examples that characterize each of these two types. We will focus on the actual infinity, with which we will discuss some of the challenges found in the theory created by Cantor on this subject. We will also show its importance and the difference between this and the potential infinity. Thus, we seek to make teachers properly understand the mathematical foundations necessary for them to work, teach and properly motivate their students at the time the infinity and infinite sets are discussed in class. In this way, we seek to clarify the terms used and common mistakes made by students and also teachers, so often misguided or confused by common sense.
 
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Publishing Date
2015-04-08
 
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