Relacije ekvivalencije i cijeli brojevi

master's thesis

• Title (english): Equivalence relations and integers
• Author: Iva Kovačić
• Mentor: Goran Muić (mentor)
• Committee member: Goran Muić (predsjednik povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu se najprije prisjećamo pojma relacije, te aksioma na temelju kojih je izgrađen skup prirodnih brojeva. Potom proučavamo jednu specifičnu relaciju, relaciju ekvivalencije i njezina svojstva te način na koji konstruiramo i izgrađujemo skup cijelih brojeva \(\Z\). Također, proučavamo algebarsku strukturu i svojstva osnovnih računskih operacija na skupu cijelih brojeva.

Abstract (english)

In this thesis, firstly, we introduce the notion of relation and the Peano axioms on which the set of natural numbers was built. Then, we study one specific relation, which is the relation of equivalence, used in our construction of the set of integers \(\Z\). Also, we study the algebraic structure and properties of elementary arithmetic operations on a set of integers.

• Keywords: prirodni brojevi; algebarska struktura; skup cijelih brojeva
• Keywords (english): natural numbers; algebraic structure; a set of integers
• Language: croatian
• URN:NBN: urn:nbn:hr:217:847937
• 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: 2024-02-02 08:43:59