Konstrukcija realnih števil

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2013
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[R. Grešak]
UDK:	51(043.2)
COBISS:	9801801
Št. ogledov:	1243
Št. prenosov:	195
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Construction of the real numbers
Sekundarni povzetek:	In this thesis, there are described two standard constructions of the real numbers, these are the construction of real numbers via Dedekind cuts and the construction with metric fill of the rational numbers. Rational numbers are already a linearly ordered commutative field, so we first list the axioms of a linearly ordered commutative field. Then we take a look to the Dedekind's axiom, which only applies to real numbers and distinguishes between real and rational numbers. In thesis, there are proven some of these axioms. Beside that we prove the uniqueness theorem, which says that the set that satisfies axioms in linearly ordered commutative field, is unique up to isomorphism. Because these two constructions are quite complicated, we end thesis with method, how to explain construction of the real numbers to the secondary school students.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo/naloga
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Matematika-računalništvo
Strani:	23 str.
Vrsta dela (ePrints):	thesis
Naslov (ePrints):	Construction of the real numbers
Ključne besede (ePrints):	realna števila
Ključne besede (ePrints, sekundarni jezik):	real numbers
Povzetek (ePrints):	V diplomskem delu sta opisani dve standardni vpeljavi realnih števil, to je vpeljava s pomočjo Dedekindovih rezov in vpeljava z metrično napolnitvijo racionalnih števil. Že racionalna števila so linearno urejen komutativen obseg, zato najprej naštejemo aksiome v linearno urejenem komutativnem obsegu. Nato si ogledamo Dedekindov aksiom, ki velja le za realna števila in tako loči med realnimi in racionalnimi števili. V diplomskem delu je dokazanih nekaj teh aksiomov. Poleg tega pa dokažemo še izrek o enoličnosti realnih števil, ki pove, da je množica, ki zadosti aksiomom za linearno urejen komutativni obseg, do izomorfizma natančno ena sama. Ker sta ti dve vpeljavi precej zapleteni, si na koncu ogledamo še način, kako razložiti vpeljavo realnih števil dijakom v srednjih šolah.
Povzetek (ePrints, sekundarni jezik):	In this thesis, there are described two standard constructions of the real numbers, these are the construction of real numbers via Dedekind cuts and the construction with metric fill of the rational numbers. Rational numbers are already a linearly ordered commutative field, so we first list the axioms of a linearly ordered commutative field. Then we take a look to the Dedekind's axiom, which only applies to real numbers and distinguishes between real and rational numbers. In thesis, there are proven some of these axioms. Beside that we prove the uniqueness theorem, which says that the set that satisfies axioms in linearly ordered commutative field, is unique up to isomorphism. Because these two constructions are quite complicated, we end thesis with method, how to explain construction of the real numbers to the secondary school students.
Ključne besede (ePrints, sekundarni jezik):	real numbers
ID:	8311800