Números algébricos e transcendentes.

Abstract

The present monography addresses the algebraic numbers and transcendental numbers, and aims to arouse the interest of the interlocutor about these singular numbers. Furthermore, it seeks to serve as an in-depth study of the subject, stating definitions, important results and some interesting facts. In a first moment, introductory concepts of algebraic and transcendental numbers along with examples are brought forward. Then, we get into results and indispensable themes when it comes to studying transcendental numbers, such as enumerability, the transcendental nature of Euler’s number, rational approximation, Liouville numbers and Riemann zeta function. This last one is among the most important functions of mathematics because it is related to Riemann hypothesis, which is considered by some to be one of the most relevant problems in math.