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A '''set''' is a collection of objects.  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} because order does not matter when comparing sets.

A '''set''' is a collection of objects.  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 <math>\{1,2\}</math> indicating the set containing the elements 1 and 2. This is the same as the set <math>\{2,1\}</math> because order does not matter when comparing sets.

Also, repetition of elements is irrelevant, so the set {1, 2, 2} is the same as the set {1, 2}.

Also, repetition of elements is irrelevant, so the set <math>\{1,2,2\}</math> is the same as the set <math>\{1,2\}</math>.

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.   

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 <math>\{1,2\}</math> 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.

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.