Ordinalna in kardinalna števila : magistrsko delo

Peharc, Lana (author), Slapar, Marko (mentor)

V magistrskem delu bom predstavila ordinalna in kardinalna števila. Na začetku bodo predstavljene nekatere osnovne definicije in izreki teorije množic. Ti nam bodo pomagali pri razumevanju konceptov, ki bodo sledili. Predstavila bom tudi Zermelo-Fraenklov aksiomatski sistem in aksiom izbire. Nekaj besed bo namenjenih naravnim številom in njihovi razlagi v sklopu teorije množic. Pomembno vlogo bodo imele dobro urejene množice in urejenost na množicah, ki bodo predstavljene v nadaljevanju. Osrednji del magistrske naloge bo predstavljala razlaga ordinalnih in kardinalnih števil.

• Language: Slovenian
• Keywords: Ordinalna števila, kardinalna števila, kardinalnost, urejene množice, dobra urejenost
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Place of publishing: Ljubljana
• Publisher: L. Peharc
• Year: 2024
• Number of pages: 43 str.
• PID: 20.500.12556/RUL-159719
• UDC: 510.3(043.2)
• COBISS.SI-ID: 202403843
• Publication date in RUL: 19.07.2024

Secondary language

• Language: English
• Title: Ordinal and cardinal numbers

Abstract

In my master's thesis, I will present ordinal and cardinal numbers. I will start with some basic definitions and theorems of set theory. These will help us understand the concepts that will follow. I will also present the Zermelo-Fraenkl axiomatic system and the axiom of choice. A few words will be devoted to the natural numbers and their interpretation within set theory. An important role will be played by well-ordered sets and order on the sets, which will be presented next. The central part of the master's thesis will be the interpretation of ordinal and cardinal numbers.

• Keywords: Ordinal numbers, cardinal numbers, cardinality, ordered sets, well-ordered sets