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Mängdlära
1998 (Swedish)Independent thesis Advanced level (degree of Master (One Year))Student thesis
Abstract [en]

The essay is firstly on Cantor’s set theory and secondly on Zermelo-Fraenkel’s axiom system. After a historical introduction it starts with Cantor’s definition, which briefly means that every collection of objects into a whole – is a set. It is not used in axiomatic set theory, because it leads to paradoxes, however, they normally do not occur. Subsets, unions, intersections, functions, equivalence relations and order relations are exposed. Next chapter is about the natural number sequence including Peano’s axioms. Later the concepts of cardinal and ordinal number are introduced. One section treats the axiom of choice. The succeeding chapter is about Zermelo-Fraenkel’s axiom system with the improvements of John von Neumann. It also includes his theory of cardinals and ordinals. They are sets and so are the natural numbers. The last chapter is a biography of Georg Cantor, who created the infinite set theory. Keywords Russell Natural numbers Cardinals Ordinals Infinity Cantor Zermelo Set Nyckelord Russell Naturliga tal Kardinaltal Ordinaltal Oändligheten Cantor Zermelo Mängd

Place, publisher, year, edition, pages
1998. , 61 p.
Identifiers
URN: urn:nbn:se:kau:diva-54799Local ID: MAT D-1OAI: oai:DiVA.org:kau-54799DiVA: diva2:1104563
Subject / course
Mathematics
Available from: 2017-06-01 Created: 2017-06-01

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