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A Brief Introduction to Set Theory for High Schools
 Weber, David ; Rmoutil, Martin (advisor) ; Škorpilová, Martina (referee)
This thesis gives an explanation of the basic concepts of set theory, focusing primarily on high school students interested in mathematics. The text of the thesis is di- vided into six chapters. The first chapter provides a historical context, mainly explaining the development of the term "infinity" and the reasons for the establishment of axiomatic set theory. The second chapter reminds the reader of propositional logic and gives a sim- plified explanation of predicate calculus. Main focus of this chapter is on the explanation of working with logical quantifiers. The third chapter deals with the Zermelo-Fraenkel set theory axioms and some basic properties about sets they imply. Chapter Four separately introduces relations and related terminology, especially mappings and their properties. The penultimate chapter shows how to establish natural numbers using sets. In its in- troductory part, it is concisely presented a method of such establishment by means of Peano axioms. Further on, the knowledge concerning relations are extended along with the definition of ordering and ordered sets, and some basic properties of natural numbers in context of the described establishment are proved. The last chapter is devoted to the problem of comparing infinite sets. The idea of Hilbert hotel, comparison of sets...
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