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master's thesis
Ordinalni kalkulator
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:746025
Bašić, Bjanka
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Bašić, B. (2020). Ordinalni kalkulator (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:746025

Bašić, Bjanka. "Ordinalni kalkulator." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:746025

Bašić, Bjanka. "Ordinalni kalkulator." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:746025

Bašić, B. (2020). 'Ordinalni kalkulator', Master's thesis, University of Zagreb, Faculty of Science, accessed 28 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:746025

Bašić B. Ordinalni kalkulator [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 28] Available at: https://urn.nsk.hr/urn:nbn:hr:217:746025

B. Bašić, "Ordinalni kalkulator", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:746025

Metadata
TitleOrdinalni kalkulator
AuthorBjanka Bašić
MentorVedran Čačić (mentor)
Committee memberVedran Čačić (predsjednik povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu razvili smo računalnu reprezentaciju ordinala do \(\epsilon_0 \) u Cantorovoj normalnoj formi. Nad njome smo implementirali uspoređivanje te operacije zbrajanja, množenja i potenciranja u sklopu programa OrdCalc. U prvom poglavlju smo se upoznali s raznim klasama uređenih skupova te pojmom ordinalnog broja. U drugom poglavlju smo definirali navedene relacije i operacije te dokazali njihova osnovna svojstva. Posebno smo dokazali apsorcijsko svojstvo za zbrajanje i množenje. Također smo dokazali teoreme o oduzimanju i dijeljenju na kojima se temelji implementacija tih dviju operacija. U zadnjem poglavlju smo koristeći razvijenu aritmetiku ordinala izveli algoritme za ostale operacije na kojima se temelji njihova implementacija u Ordinalnom kalkulatoru.
Abstract (english)
In this paper, we have developed a computer representation of the ordinals up to \(\epsilon_0 \) in Cantor’s normal form. Using it we have implemented comparison, addition, multiplication and exponentiation as a part of the OrdCalc program. In the first chapter, we introduced various classes of ordered sets and the concept of ordinal number. In the second chapter, we defined the mentioned relations and operations and proved their basic properties. In particular, we proved the absorption property of addition and multiplication. We also proved the subtraction and division theorems on which the implementation of these two operations is based. In the last chapter, using the developed ordinal arithmetic, we derived algorithms for other operations on which their implementation in the Ordinal Calculator is based.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:746025
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-12-01 13:22:50