prikaz prve stranice dokumenta Peanove trojke
  Download
PDF 275.26 KB
master's thesis
Peanove trojke
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:866107
Čučić, Katarina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čučić, K. (2021). Peanove trojke (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:866107

Čučić, Katarina. "Peanove trojke." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:866107

Čučić, Katarina. "Peanove trojke." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:866107

Čučić, K. (2021). 'Peanove trojke', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:866107

Čučić K. Peanove trojke [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:866107

K. Čučić, "Peanove trojke", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:866107

Metadata
TitlePeanove trojke
Title (english)Peano triples
AuthorKatarina Čučić
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
Committee memberŽeljka Milin Šipuš (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-03-04, 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
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:866107
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-24 09:26:48