Theoretical arithmetic. Tutorial. 3rd edition. Arnold I.V.

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 a quantitative natural number on 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 Dedecinda cross -sections, the converging sequences of the cantor and adjacent the theory of steppe, indicative and logarithmic functions; 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 a 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, can be distracted from individual introductory phrases, directly start reading the corresponding paragraphs Books.

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 adjacent to it (including Abel theorem), then to the theory of E-Enlarms, the theory of natural indicative function, And also to the doctrine of divisibility, in which the concept of the smallest multiple (and not of the largest general divider, as usual) and the attitude of divisibility for fractional numbers are based. This also includes to a certain extent, which is somewhat different from the usual presentation of the theory of quantitative natural number.

The book is intended for students of the 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.