Abstract:

We want to provide some ideas for creating a number system's basic set, including the simplest structure, lexicographic sorting. In the first grade of secondary schools, students are already familiar with the set of natural numbers, integers, and rational numbers. However, creating the concept of a real number would require a coordinated arrangement of several structures (which we will not undertake in this paper). This time, the emphasis is on getting to know the infinite decimal form of irrational numbers, as this is the main feature of these numbers. Their decimal forms well characterize irrational numbers since infinite non-intermittent decimal fractions can only express irrational numbers. Within this, we strive to present non-periodicity and make it understand based on experience. Specifically, by tossing coins and matchboxes, we try to indicate the probability of the occurrence of certain events. Although these tasks are not probative, the conclusions drawn from them are not useless in developing the concept of irrational numbers. Concretely, we think of the non-intermittency of infinite decimal fractions. Then, by dragging slips of paper with digits on them, we make our students discover a minimal probability of a drag sequence in which a particular group of numbers would be constantly repeated. The tasks are primarily based on gaining experience, where we strive for a change in attitude in students. Current textbooks do not include assignments of this type. Instead of concrete examples, which would facilitate understanding, there is only a definition of irrational numbers.

Keywords:

Irrational numbers, Probability, Infinite decimals, Gaining experience.