POSSIBLE METHOD FOR ENUMERATION OF BINARY ELEMENTS

Abstract

One of the methods used to identify which sequences correspond in bijection with the set of Naturals is the Diagonalization, originally developed by the mathematician George Cantor. Diagonalization is commonly considered as proof, demonstrates that set of Binaries is not numerable and that the cardinality of Binaries and Naturals are different. However, in this work, the indications of a means of establishing a relationship between Binary elements and elements of the Naturals are pointed out, for this feat is used principle of good order, combinatorial analysis and theory of sets. Two statements were established, in the first it was considered relevant the number of houses that define a binary element as well as the associated value, in the second statement, only the associated value was considered relevant. In both statements, the enumeration of binaries was reached. Such results could represent a new method for enumerating binary sequences and possibly the other infinite sequences. The sets of Rational and Natural were also studied using this method.