Teoria dos conjuntos: um estudo introdutório
The present text introduces Axiomatic Set Theory of Zermelo-Fraenkel with Axiom of Choice. Set Theory serves as a foundation for several areas of Mathematics. From axioms and basic constructions like relations, functions and partitions, we define the set of natural numbers, we develop the notions of...
| Autor principal: | Vasconcelos, Vinícius Franco |
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| Formato: | Trabalho de Conclusão de Curso (Graduação) |
| Idioma: | Português |
| Publicado em: |
Universidade Tecnológica Federal do Paraná
2021
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| Assuntos: | |
| Acesso em linha: |
http://repositorio.utfpr.edu.br/jspui/handle/1/23976 |
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| Resumo: |
The present text introduces Axiomatic Set Theory of Zermelo-Fraenkel with Axiom of Choice. Set Theory serves as a foundation for several areas of Mathematics. From axioms and basic constructions like relations, functions and partitions, we define the set of natural numbers, we develop the notions of ordinal numbers and cardinal numbers, as well as their arithmetics, we construct the cumulative hierarchy of sets and we approach some concepts of Model Theory. It is an introductory development, with out pretension to be a complete work, but with the purpose to help studies of people attracted by Set Theory. |
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