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A '''set''' is a property of [[numbers]] which can be thought of as an object but without altering their properties. However Russell's [[paradox]] states that there are no "normal" sets, insofar as they would not be contained in itself, leading to a contradiction.

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.

 

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

 

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 [[Bertrand Russell's]] 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]]

[[Category:Mathematics]]