The natural numbers are presented first in the master's thesis. We introduced them through Pean axioms. With all five axioms we gradually show the arithmetic operations of addition and multiplication and their basic characteristics (neutral element, commutative, associative and distributive properties). The recursively defined sequences, order of natural numbers and subtraction and division, which are only partially defined operations in natural numbers, are also presented. A great emphasis is on accurate proofs of basic properties of natural numbers only with the help of Pean axioms. In the chapter about sets we focused our attention to the system of ZFC axioms, which got their names after mathematicians Zermel and Fraenkel and the axiom of choice (C). With the help of axiomatic of the theory of sets (mainly axiom of infinity) we introduce natural numbers like a set in which we show validity of Pean axioms. In the last part of the thesis we also introduced integers and rational numbers like quotient sets of the Cartesian product N×N or Z×Z\\{0}.
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