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Title:Preštevanje racionalnih števil
Authors:ID Konec, Nuška (Author)
ID Banič, Iztok (Mentor) More about this mentor... New window
ID Vesel, Aleksander (Comentor)
Files:.pdf UNI_Konec_Nuska_2010.pdf (538,27 KB)
MD5: 4B3F3290F9B1A30FBEF03061070B0E36
PID: 20.500.12556/dkum/3322a2f4-42ce-4652-850e-4b6ca76ef840
 
Language:Slovenian
Work type:Undergraduate thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V uvodu bomo spoznali pojme, ki so bistveni za razumevanje diplomske naloge. Tako se bomo seznanili z definicijo števne množice, izvedeli nekaj o grafih in drevesih, spoznali metodi iskanja v neskončnih drevesih, predstavljena pa je tudi rekurzija oz. rekurzivna zveza. V poglavju Preštevanje racionalnih števil bomo spoznali načine, s katerimi lahko dokažemo števnost racionalnih števil. To so: osnovni zgled, Calkin-Wilfovo drevo, preštevanje racionalnih števil s pomočjo največjega skupnega delitelja ter s pomočjo razcepa na prafaktorje.
Keywords:Racionalna števila, graf, Calkin-Wilfovo drevo, največji skupni delitelj.
Place of publishing:Maribor
Publisher:[N. Konec]
Year of publishing:2010
PID:20.500.12556/DKUM-14989 New window
UDC:51(043.2)
COBISS.SI-ID:17833736 New window
NUK URN:URN:SI:UM:DK:IDWH4R99
Publication date in DKUM:06.09.2010
Views:2807
Downloads:174
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:Counting the rationals
Abstract:In the beginning we will present the terms that are crucial for the understanding of this diploma thesis. We will present the definition of a countable set, explain graphs and trees and show two methods of searching within the infinite trees. We will also define recursion which is also called the recursive connection. In the chapter Counting the rationals we will show different proofs showing that rationals are countable. These are: the basic example, Calkin-Wilf tree, counting the rationals with the help of the greatest common divisor and with the help of splitting the numbers on primes.
Keywords:Rationals, graph, Calkin-Wilf tree, greatest common divisor.


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