Kardinalnost skupova

master's thesis

• Author: Danijela Protega
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Committee member: Vedran Čačić (član povjerenstva)
• Committee member: Zoran Vondraček (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Rad je podijeljen u četiri poglavlja. Prvo poglavlje je o konačnim i prebrojivim skupovima u kojem smo definirali neke pojmove te iskazali i dokazali neke tvrdnje koje predstavljaju osnovu za daljnje razumijevanje. U drugom poglavlju govorimo o kardinalnim brojevima. Kako bismo definirali kardinalni broj, govorimo o nepostojanju skupa svih skupova i uvodimo pojam klase. Kao važniju tvrdnju ovog poglavlja dokazujemo Cantor-Schröder-Bersteinov teorem te iznosimo osnovne operacije s kardinalnim brojevima. U trećem poglavlju definiramo neke osnovne matematičke pojmove i dokazujemo bitne tvrdnje iz matematičke analize koje su nam važne za ključne tvrdnje ovog poglavlja. Za kraj, četvrto poglavlje započinje s definicijom binarne relacije. U njemu govorimo o dobro uređenim skupovima te dolazimo do usporedivosti kardinalnih brojeva, o kojoj nam govori zadnja važna tvrdnja ovog diplomskog rada.

Abstract (english)

This thesis is divided into four chapters. The first chapter deals with finite and infinite countable sets in which we defined some notions and stated and proved some statements which represent the foundation for the further understanding. In the second chapter we are dealing with cardinal numbers. To define cardinal number, we are proving that set of all sets does not exist and we are introducing the notion of a class. As important statement of this chapter, we are proving the Cantor-Schröder-Berstein theorem and providing basic operations with cardinal numbers. In the third chapter we are defining some basic mathematical notions and proving important statements from the field of mathematical analysis which are of great importance for this chapter. In the end, the forth chapter starts with the definition of a binary relation. This chapter deals with well-ordered sets and comparability of cardinal numbers which is especially mentioned in the last important statement of this thesis.

• Keywords: konačni i prebrojivi skupovi; kardinalni brojevi; Cantor-Schröder-Bersteinov teorem; binarna relacija
• Keywords (english): finite and infinite countable sets; cardinal number; Cantor-Schröder-Berstein theorem; binary relation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:695612
• 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: 2019-06-12 12:22:36