Teoria dos conjuntos e o axioma da escolha

Abstract

The present work is a brief study on the theory of sets, highlighting a historical line of events that culminated in the creation of the ZFC axiomatic system. It is shown the importance of defining what sets are made visible and that the informal definition existing up to the beginning of the twentieth century was not capable of producing a coherent mathematics. For this, some paradoxes caused by naive definitions previously used are described. Among the axioms of the axiomatic system ZFC, which proposes the establishment of well-specified rules for the formation of sets, the axiom of choice stands out. In the paper we present the historical context in which the emergence of the axiom of choice is inserted, the definition, the equivalences and the generated paradoxes (mentioned). The work completes a classroom application based on concepts that have emerged in the development of this, such as paradoxes, axioms and infinity. The target audience was the Neja students (modules 3 and 4) of the State College Natividade Patrício Antunes - Nova Iguaçu - Rio de Janeiro. The purpose of this application was to present these concepts, little explored in high school, through an accessible language and to analyze statistically the students' knowledge before and after the proposed didactic sequence. Despite the difficulties of the students in interpretation and writing, there was a significant improvement in relation to the understanding of the proposed concepts