Teoria de conjuntos: um estudo sobre suas propriedades e aplicações

Abstract

Set Theory studies the grouping of elements that have common characteristics or properties, being of great importance for its application in Mathematics as well as in other sciences. The definitions, properties and theorems that are described in this essay are intended to provide a well-founded and concise structuring, avoiding contradictions or gaps regarding their applications. Through examples and demonstrations, we make clear that not only the concepts relevant to the study of sets can be useful in science, but also set operations combined with sentence logic are of great value, as they underlie an entire structure of thought used in scientific area. Thus, this work aims to analyze the application of Set Theory in Mathematics and in other areas of science, being helpful as an instrument of conceptual appropriation. Therefore, we searched the literature for a theoretical foundation on the topic and its applicability in di erent situations that require disciplinary approach. Finally, we hope that this study will be an instrument of investigation and understanding in an area that has an important role as a guide in mathematical and scienti c research.