Integration of discreteness and continuity in forming mathematical world view among students

Introduction. When studying mathematics the principle of a wholeness of contents, of integration of its separate components is not always followed. The problem is in how to give students not just the sum of knowledge of separate elements of mathematics, but some holistic integrated system of ideas of the world of mathematics. The purpose of the article is to consider the way of forming an integral mathematical world view. Materials and Methods. To solve the problem, the article draws on philosophical views on the scientific picture of the world as a special form of systematization and integration of knowledge, as well as a trinitarian methodology and historical analysis. The trinitarian methodology has been increasingly used in the post-non-classical worldview. This methodology presupposes the presence of the third element in addition to two binary oppositions, which is necessary to solve the problem of binary contradictions, their integration into a single whole, as a measure of their compromise, as an arbitrator, as a condition for their existence. Results. Based on the trinitarian methodology, the article shows that the unity of discreteness and continuity, the possibility of their integration into a single whole can be provided with the help of a fractality as the third component. The fractality is just as fundamental structural property of a matter as discreteness and continuity. Thus, it is shown that fractal geometry is not just a new branch of mathematics, it is one of the most important components of the mathematics' world view of. By studying this section, it is possible when teaching mathematics to students the integration of continuity and discreteness, to develop a holistic intergrated mathematical world view in students. Discussion and Conclusions. For practical work in high school and university, it is also important that the study of fractal geometry contributes to the solution of the main tasks set in the concept of Development of Mathematical Education in Russia. This is primarily to improve students' motivation to study mathematics, developing cognitive activity among them, bringing together the learning and research, and solving the problem of the aesthetic orientation of education. Fractal geometry is also a means of integration in the teaching of mathematics and information technology. Therefore, there are all grounds for introducing schoolchildren and students to it.