Construção dos números reais via cortes de dedekind.
This monograph has as main objective the construction of the real numbers via cuts of Dede- kind. To do so, we will discuss the characterization of the set of natural numbers N by the Peano axioms and, from the natural numbers, we will construct the set of integers Z via equivalence relation in N×...
| Autor principal: | CAVALCANTE, Daniel Alves |
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| Grau: | Monografia |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Tocantins
2023
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| Assuntos: | |
| Acesso em linha: |
http://hdl.handle.net/11612/5123 |
| Resumo: |
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This monograph has as main objective the construction of the real numbers via cuts of Dede-
kind. To do so, we will discuss the characterization of the set of natural numbers N by the Peano axioms and, from the natural numbers, we will construct the set of integers Z via equivalence
relation in N×N. Then, also via equivalence relation, we will construct the set of rational num-
bers Q and present some of the properties of its elements. In order to reach our research goal,
we will show the insufficiency of Q to measure some line segments. Then, we will construct
the set of real numbers R from the Dedekind cuts and we will present the main properties of
this set, especially highlighting the one that differs from Q. |