Introdução aos números transcendentes e aos números de Liouville

Abstract

The Theory of Transcendental Numbers is an area that was originated by Joseph Liouville in his illustrious work of 1844, in which he created a numerical class, the Liouville Numbers, by which he not only proved the existence of transcendental numbers, as well as his first examples. In this sense, this work aims to develop a study on the Theory of Transcendental Numbers, specifically the Liouville Numbers. This study was carried out through a qualitative research, constituting a bibliographic study. Among the main results, we highlight the definition and characterization of the set of algebraic numbers and transcendental numbers, and the presentation of important results on the class of Liouville Numbers. In this perspective, this work presents itself as a small “research” in Transcendental Theory, whose importance lies in subsidizing future studies in a way that supports its theoretical progress in the scientific environment, since it is a recent area that has aroused interest of many researchers.