Potpunost i njene posljedice

master's thesis

• Author: Kristina Tkalec
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavamo potpunost polja realnih brojeva te posljedice koje ta potpunost ima na svojstva neprekidnih funkcija. U prvom poglavlju uvodimo realne brojeve te potrebne algebarske pojmove kao što su grupe i prsteni. U drugom poglavlju proučavamo neprekidne funkcije. Dokazujući potrebne teoreme i propozicije, na posljetku dolazimo do konačnog zaključka: slika neprekidne funkcije na segmentu je segment. Pristup koji smo koristili nije zahtijevao uvođenje prirodnih brojeva

Abstract (english)

In this diploma thesis we study the completeness of the field of real numbers and the consequences of this completeness on properties of continuous functions. In the first chapter we introduce the real numbers and necessary algebraic notions such as the notion of a group and the notion of a field. In the second chapter we study continuous functions. By proving necessary theorems and propositions we come to the final conclusion: the image of a continuous function on a segment is a segment. The approach that we used did not require the introduction of natural numbers.

• Keywords: potpunost polja realnih brojeva; neprekidne funkcije; grupe; prsteni
• Keywords (english): completeness of the field of real numbers; continuous function; groups; rings
• Language: croatian
• URN:NBN: urn:nbn:hr:217:904261
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-15 08:26:38