View source for Permutation of a set

{{Stub page|grade=A*|msg=Very important to get some work on the symmetric group in play, then this may be demoted. Demote to grade A once the notation section has been added, there's a lot to say there.}}
: '''Note: ''' [[permutation on a set]] redirects here.
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==Definition==
Let {{M|X}} be any ''non-empty'' [[set]], {{M|X}}. A ''permutation'' on {{M|X}}{{rRFAGRBJTA}}{{rAAPAG}} is:
* A ''[[bijective]]'' [[function]], {{M|f:X\rightarrow X}}. Recall that bijective means [[injective]] (1:1) and [[surjective]] (onto).
'''Claims:'''
: [[The collection of all permutations of a set forms a group under function composition]] - see the [[permutation group]]. The [[symmetric group]] is a special case of the permutation group when the set is finite.
==References==
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{{Definition|Abstract Algebra|Set Theory|Group Theory}}