Theoretical arithmetic

The book consists of two parts - the teachings of the number in its consistent generalizations and the initial chapters of the theory of numbers in the usual sense of the word. Here the reader will find: the theory of the quantitative number of the cantor, the theory of natural numbers and the bilateral natural series of the grassman, the theory of steam for the introduction of negative, fractional and complex numbers, the theory of Dedekind"s cross -sections, the convergent cantor"s sequences and the theories of steppe, indicative and logarithmic functions, the theory Further, brief information about transfinite numbers stated in connection with the doctrine of the natural number, the theory of quaternions exponentially and elementary information from the theory of hypercomplex numbers in the amount necessary for the proof of the Frobenius theorem, in a certain sense of the final doctrine of the numerical field in connection with it. a generalization of the concept of number.
All of the above material is highlighted in the text so that the reader who wants to get acquainted with a particular theory, regardless of the main thread of the presentation, may, distracted from individual introductory phrases, directly begin to read the corresponding paragraphs of the book.
The rest of the book contains a material related to the operator theory of number and measurement and to the theory of operations of the highest steps (including Abel theorem), then to the theory of E-Enlarms, the theory of natural indicative function, as well as to the teachings of about Divisability, which is based on the concept of the smallest multiple (and not the largest general divider, as usual) and the attitude of divisibility for fractional numbers. This also includes to a certain extent somewhat different from the usual presentation of the theory of quantitative natural number.
The book is intended for students of physical and mathematical faculties of pedagogical universities. The manual will also be useful to teachers of relevant disciplines, mathematics teachers and everyone who is interested in the teaching of the number and theory of numbers