Peanove trojke

master's thesis

• Title (english): Peano triples
• Author: Katarina Čučić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Željka Milin Šipuš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-03-04, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu smo pručavali Peanove trojke. U prvom poglavlju smo najprije opisali osnovne pojmove vezane za funkciju potrebne za ovaj rad. Nadalje, definirali smo pojam Peanove trojke i proučili neka njena svojstva između kojeg je i dokaz principa definicije indukcijom. U nastavku rada smo definirali zbrajanje i uređaj na Peanovoj trojci uz njihova osnovna svojstva. Za kraj prvog poglavlja definirali smo izomorfizam i proučili ga u okviru Peanovih trojki dokazavši i ujedno da su svake dvije Peanove trojke izomorfne. Drugo poglavlje je bilo posvećeno beskonačnim skupovima. Uz pretpostavku da postoji beskonačan skup dokazali smo egzistenciju Peanove trojke. Potom smo i dokazali egzistenciju beskonačnog skupa uz pretpostavku postojanja novouvedenih p-skupova. Dotakli smo se i teme ekvipotentnosti skupova. Koristeći Peanove trojke karakterizirali smo beskonačne skupove. Na kraju smo iskazali i dokazali neke od činjenica vezanih za konačne skupove.

Abstract (english)

In this Master’s Thesis Peano triples were discussed. First chapter started with definition of a function and its main properties that were necessary for this Thesis. Then we defined Peano triples and studied some of its characteristics, main one being the definition by induction. Furthermore, by using Peano triples addition and inequality were introduced. Final topic of first chapter was isomorphism where we proved that any two Peano triples are isomorphic. Chapter two was dedicated to infinite sets. By assuming that an infinite set exists we proved existence of a Peano triple. Afterwards, we also demonstrated existence of an infinite set with the assumption that p-sets exist. Then we observed equipotent sets. Using Peano triples we characterized infinite sets. At the very end, we stated and proved some of the properties of finite sets.

• Keywords: Peanove trojke; izomorfizam; beskonačni skupovi
• Keywords (english): Peano triples; isomorphism; infinite set
• Language: croatian
• URN:NBN: urn:nbn:hr:217:866107
• 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: 2021-03-24 09:26:48