p-adične norme in p-adična števila

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2014
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[I. Femc]
UDK:	511(043.2)
COBISS:	10203977
Št. ogledov:	851
Št. prenosov:	179
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	p-adic norms and p-adic numbers
Sekundarni povzetek:	We can construct rational numbers Q as a quotient set of pairs (a, b) where a and b are integers or we can define fractions a/b, where b is not equal to 0. Two fractions a/b and c/d represent the same number if and only if ad=bc. In this thesis, we firstly describe absolute values on rational numbers Q: usual absolute value, trivial absolute value and p-adic absolute value. Then we prove the Ostrowski theorem, which says that every non-trivial absolute value on Q is equivalent to either usual absolute value or the p-adic absolute value for some prime number p. The metric space of rational numbers Q is complete with respect to the trivial absolute value. We know, however, that rational numbers Q are not complete with respect to the usual absolute value. We can extend the space of rational numbers Q with respect to the usual absolute value to get the space of real numbers, which is a complete metric space. If we take any p-adic absolute value on rational numbers Q instead of the usual absolute value, we get the metric space which is also not complete. The metric completion of this metric space is called p-adic numbers. We end the thesis with some characteristics of p-adic integers and prove the p-adic expansion of p-adic numbers.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo/naloga
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Dvopredmetni učitelj
Strani:	20 str.
ID:	8680355