Abstract
The article is devoted to the study of the peculiarities of
 real numbers in the discipline "Algebra and analysis" in the secondary
 school. The theme of "Real numbers" is not easy to understand
 and often causes difficulties for students. However, the study of this
 topic is now being given enough attention and time. The consequence
 is a lack of understanding of students and school-leavers, what
 constitutes the real numbers, irrational numbers. At the same time
 the notion of a real number is required for further successful study
 of mathematics. To improve the efficiency of studying the topic
 and form a clear idea about the different numbers offered to add
 significantly to the material of modern textbooks, increase the
 number of hours in the study of real numbers, as well as to include
 in the school course of algebra topics "Complex numbers" and
 "Algebraic structures".
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