Preštevanje racionalnih števil

diplomsko delo

Nuška Konec (Author), Iztok Banič (Mentor), Aleksander Vesel (Co-mentor)

Abstract

V uvodu bomo spoznali pojme, ki so bistveni za razumevanje diplomskega dela. 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 in s pomočjo razcepa na prafaktorje.

Keywords

matematika;racionalna števila;preštevanje;grafi;skupni delitelj;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Konec]
UDC:	51(043.2)
COBISS:	17833736
Views:	2102
Downloads:	108
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Counting the rationals
Secondary 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.
Secondary keywords:	Rationals;graph;Calkin-Wilf tree;greatest common divisor.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	48 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18745