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master's thesis
Konačnost i aksiomi prirodnih brojeva
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:656283
Milković, Kristina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Milković, K. (2017). Konačnost i aksiomi prirodnih brojeva (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:656283

Milković, Kristina. "Konačnost i aksiomi prirodnih brojeva." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:656283

Milković, Kristina. "Konačnost i aksiomi prirodnih brojeva." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:656283

Milković, K. (2017). 'Konačnost i aksiomi prirodnih brojeva', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:656283

Milković K. Konačnost i aksiomi prirodnih brojeva [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:656283

K. Milković, "Konačnost i aksiomi prirodnih brojeva", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:656283

Metadata
TitleKonačnost i aksiomi prirodnih brojeva
AuthorKristina Milković
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberVjekoslav Kovač (član povjerenstva)
Committee memberDragutin Svrtan (član povjerenstva)
Committee memberZvonimir Tutek (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-07-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu proučavali smo skup prirodnih brojeva te pojam konačnog i prebrojivog skupa. U prvom smo poglavlju, krenuvši od aksioma, uveli osnovne pojmove vezane uz skup prirodnih brojeva kao što su zbrajanje prirodnih brojeva i uređaj na skupu prirodnih brojeva te smo dokazali neke činjenice vezane uz to. Također, iskazali smo i dokazali princip definicije indukcijom. U drugom smo poglavlju uveli pojam konačnog skupa te dokazali osnovne činjenice vezane uz to. Nadalje, proučavali smo beskonačne skupove te dokazali da je skup beskonačan ako i samo ako je ekvipotentan svom pravom podskupu. Pojam prebrojivog skupa je bio središnji pojam trećeg poglavlja. Ispitivali smo razna svojstva ovoga pojma te smo dokazali da je unija prebrojive familije prebrojivih skupova i sama prebrojiva. Navedeni pojmovi imaju važnu ulogu u teoriji skupova, što je prikazano i u ovom diplomskom radu.
Abstract (english)
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:656283
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-03-01 11:42:00