Difference between revisions of "Set"

Revision as of 00:43, August 31, 2008

A set is a collection of distinct objects. No element may appear more than once in a set.

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-A '''set''' is a collection of objects, and sets are the subject of [[set theory]].  Two sets are the same if they contain the same elements, regardless of the order they are in. Sets are written in set notation, such as {1,2} indicating the set containing the elements 1 and 2. This is the same as the set {2,1}, as order does not matter.
+A '''set''' is a collection of distinct objects. No element may appear more than once in a set.
-Also, repetition of elements is irrelevant, so {1,2,2} is the same as the set {1,2}.
+* Compare [[multiset]]
-An important concept in set theory is [[cardinality]]. In the case of finite sets, this is simply the number of elements of the set. So {1,2} has a cardinality of 2. However, the theory is more complicated in the case of infinite sets.
-It was thought that an informal concept of sets ([[Naive set theory]]) was sufficient, however [[Russell's Paradox]] shows that this can lead to a contradiction, if sets are allowed to contain themselves. Modern set theory is more formal, and disallows such paradoxical sets.
 [[Category:Mathematics]]