Irrational and linearly unrelated sequences.

The thesis deals with the irrationality, irrational sequences, linearly independent sums of series and linearly unrelated sequences. It is divided into 3 chapters. The 1st one is a history overview. The 1st reference of problems concerning the number theory dates back as fas as the time of the antient Greece. The majority of results in mathematics, however, belong to more modern times of the 15th century. As far as the theories of irrationality and transcendence are concerned, the turning point does not take place until 18th century. Firstly, in 1744 Euler proved the irrationality of real numbers, log a, where a is a positive rational number that is not equal to 1. Later, in 1766 Lambert proved the irrationality of the number ? and, successively, he proved the irrationality of the number e. At present, we know many more results concerning the irrationality of the real numbers. Badea, Erdos, Hancl, Sandor, Straus and others rank among mathematicians of the modern age who deal with the transcendence and irrationality. Their results are included in the 2nd chapter, which deals with the problems of irrational sequences. The rational sequences, irrational sequences and linearly unrelated sequences are defined here. The 3rd chapter presents the author's own results about linearly unrelated sequences.Available from STL Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi