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====== Permutation of $X$ ======
====Definition==== 
Let $X$ be a set.  A $\textdef{permutation}$ of $X$ is a bijection from $X$ to $X$. We can think of a permutation of $X$ as a way of rearranging the elements in $X$. The identity permutation is the permutation $id_X:X\to X$ defined by $id_X(x)=x$.


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==== Remarks ==== 
  * This is used to define the [[definition:symmetric group]] and [[permutation group]]s.


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==== $\LaTeX$ version ====
<file tex definition.permutation.tex>
%%%%%
% DEPENDENCIES 
% RequiredMacros: \newcommand{\textdef}[1]{\textit{#1}}
%%%%%
\begin{definition}
Let $X$ be a set.  A \textdef{permutation} of $X$ is a bijection from $X$ to $X$. We can think of a permutation of $X$ as a way of rearranging the elements in $X$. The identity permutation is the permutation $id_X:X\to X$ defined by $id_X(x)=x$.
\end{definition}
</file>

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==== External links ====
  * [[wp>Permutation]]


{{tag>definition needsreview ben rben rjosh}}

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