Modeli brojeva

master's thesis

• Title (english): Models of numbers
• Author: Marija Bareta
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Ivana Šain Glibić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-09-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu smo prvo dali neke činjenice iz elementarne teorije skupova, što je bio sadržaj prvog poglavlja. U njemu smo govorili o uređenim parovima, uniji i presjeku skupova, Kartezijevom produktu skupova te smo pokazali da ne postoji skup svih skupova. U drugom poglavlju smo proučavali pojmove relacije i funkcije te neka svojstva tih pojmova. Beskonačnim skupovima, Peanovim parovima te egzistencijom Peanovog para smo se bavili u trećem poglavlju. Četvrto poglavlje je bilo posvećeno pojmu skupoida. Koristeći taj pojam, dokazali smo egzistenciju beskonačnog skupa. U petom, zadnjem poglavlju, proučavali smo uređene grupe i uređene prstene te smo definirali prirodne brojeve u uređenom prstenu. Nadalje, proučavali smo potpuno uređene skupove i potpuno uređena polja, to jest polja realnih brojeva.

Abstract (english)

In this thesis, we first presented some facts from elementary set theory, which was the content of the first chapter. In it, we dealt with ordered pairs, the union and intersection of sets, the Cartesian product of sets, and we proved that there is no set of all sets. In the second chapter, we studied the notions of relations and functions and some properties of these notions. We studied infinite sets, Peano pairs and the existence of Peano pairs in the third chapter. The fourth chapter was devoted to the concept of a setoid. Using this concept, we proved the existence of an infinite set. In the fifth, last chapter, we studied ordered groups and ordered rings, and we defined natural numbers in an ordered ring. Furthermore, we studied completely ordered sets and completely ordered fields, that is, fields of real numbers.

• Keywords: elementarna teorija skupova; Kartezijev produkt skupova; Peanovi parovi; skupoid
• Keywords (english): elementary set theory; Cartesian product of sets; Peano pairs; setoid
• Language: croatian
• URN:NBN: urn:nbn:hr:217:726837
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2025-02-05 13:28:32