A não enumerabilidade do conjunto R dos números reais e a desordem no conjunto C dos números complexos

Abstract

The teaching of Real Analysis and Linear Algebra is of incalculable importance in the area of higher mathemats,ic given its wide use in the most diverse lines of research in graduate courses. Its approach in the area of topology, real numbers and vector spaces brings a contribution to parallel learning in the classroom. This text shows itself as an aid, research and cooperation instrument for the school community and, of course, strengthening the knowledge and learning of academics. There are some questions to be clari ed: It is possible to enumerate the set R of the real numbers? Is the C set of complex numbers ordered and complete? Are there non-iomorphic ordered bodies? Presenting some features and language, we show the answer to each of these questions. The text has an elementary character due to the fact that, at rst, the results were written for academic beginners of the mathematics course, although it also extended to mathematics lovers in general. The results presented here are the product of studies and seminars that were presented by academics from CEST-UEA and also from NESEIR-UEA. Keywords: Field, enumerability, real, complex.