Abstract:

Column theory has an important role in the historical development of mathematics. Zermelo-Fraenkel's theory of collections, which today helps to reveal almost all mathematical problems and develop solutions methods, has a distinct importance in the building of the foundation of the theory of collections. Despite its inclusion in mathematical practice, students have difficulties in understanding the assembly actions and well-ranged countable infinite sets. Due to the inevitable accumulation of this knowledge, the first part of the historic development of the theory of the collections was created in this article by the Q/Z section group, and then the existence was shown by the selection action of a selection function. In other words, a selection function for an infinite crowd has been applied. Instead of using a very abstract approach, appropriate approaches have been used. In addition, a complete set of sets method has been obtained. Then the infinite sets can be counted well. Finally, it has been stated that each column can be obtained well using the Zermelo-Fraenkel accium system or Zorn Lemma. These methods are taught to high school teachers. With the help of this method, students were able to identify infinite sets more easily and they were able to process these sets easily. The method of teaching, learning and evaluation to find full and well-ranged countable sets and choice action is studied as an application of group and group theory in this study. In this way, the method has increased the student’s interest in cybersecurity concepts and has contributed to the development of their mathematical knowledge and skills.

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