Konačnost i aksiomi prirodnih brojeva

In this thesis we studied a set of natural numbers and the concept of a finite and a countable set. In the first chapter, starting with the axioms, we introduced basic concepts related to a set of natural numbers such as the addition of natural numbers and the order on the set of natural numbers, and we have proven the facts related to it. We also demonstrated and proved the principle of definition by induction. In the second chapter, we introduced the concept of a finite set and we proved the basic facts related to it. Furthermore, we have studied infinite sets and we proved that a set is infinite if and only if it is equipotent to its proper subset. The countable set was the central notion of the third chapter. We examined the various properties of this concept and we proved that the union of a countable family of countable sets is countable. These notions have significant role in the theory of sets, which is shown in this thesis.