Set theory has an important place in the historical development of mathematics. This theory, which helps to reveal almost all mathematical problems and develop solution mathods with Zermelo-Fraenkel set theory, has a special importance in terms of building the base of set theory. Despite the application of mathematics, students have difficulty understanding set axioms and well-ordered countably infinite sets. Due to the inevitability of this accumulation of knowledge, firstly the historical

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... lopment of set theory has been included in this article, the ℚ/ℤ quotient group has been created, and then a choice function whose existence has been demonstrated by the choice axiom has been found. In other words, a choice function definition application has been made for an infinite set. Rather than the real method using a very abstract approach, appropriate approaches have been used. In addition, totally ordered set method was obtained. Then countably infinite sets are well-ordered. Finally, it is stated that each set can be obtained well-ordered using Zermelo-Fraenkel axiom system or Zorn's Lemma. These methods were taught to high school teachers. With the help of this method, students were able to identify infinite sets more easily and easily operate on these sets. The method of teaching, learning and evaluation of finding totally ordered and well-ordered countably sets and choice axiom has been examined in this study as an application of group and set theory. In this way, the method increased the students interest in algebraic concepts and contributed to the development of their mathematical knowledge and skills.