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master's thesis
Elementarni aspekti potpunosti
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:394596
Ćorak, Iva
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Ćorak, I. (2021). Elementarni aspekti potpunosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:394596

Ćorak, Iva. "Elementarni aspekti potpunosti." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:394596

Ćorak, Iva. "Elementarni aspekti potpunosti." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:394596

Ćorak, I. (2021). 'Elementarni aspekti potpunosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:394596

Ćorak I. Elementarni aspekti potpunosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:394596

I. Ćorak, "Elementarni aspekti potpunosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:394596

Metadata
TitleElementarni aspekti potpunosti
Title (english)Elementary aspects of completeness
AuthorIva Ćorak
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-03-05, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj diplomski rad podijelili smo na tri veća poglavlja u kojima smo promatrali neke elementarne aspekte potpunosti. Prvo poglavlje sadrži definicije osnovnih definicija, kao što su binarna operacija, binarna relacija, polje i uređaj na skupu. Na kraju prvog pogljavlja proučili smo svojstva uređenog polja. U drugom poglavlju fiksirali smo jedno potpuno uređeno polje te u njemu konstruirali skupove \(\mathbb {N}\), \(\mathbb {Z}\) i \(\mathbb { Q }\). Proučili smo svojstva tih skupova a ujedno i omeđenost. U trećem poglavlju dokazali smo da ne postoji \(\sqrt{2}\) u \( \mathbb { Q }\) a zatim smo, koristeći taj rezultat, dokazali da \( \mathbb { Q }\) nije potpuno uređeno polje. Također smo pokazali da postoji \(\sqrt{2}\) u \( \mathbb { R }\) .Na kraju smo promatrali nizove i konvergenciju nizova u uređenim poljima.
Abstract (english)
This graduate thesis is divided into three chapters through which we shown some elementary aspects of completeness. First chapter contains the basic definitions, such as binary operation, binary relation, field and order on a set. At the end of first chapter we studied some properties of an ordered field. In second chapter we fixed one complete ordered field and we constructed sets \(\mathbb {N}\), \(\mathbb {Z}\) i \(\mathbb { Q }\). We studied properties of those sets and at the same time we studied bounded sets. In third chapter we proved that there is no \(\sqrt{2}\) in \( \mathbb { Q }\) and then, using that result, we proved that \( \mathbb { Q }\) is not a complete ordered field. We also showed that there is \(\sqrt{2}\) in \( \mathbb { R }\). At the end we studied a sequence and convergence of a sequence in an ordered field.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:394596
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 on2021-03-24 09:58:24