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Definition (Permutation)
Let $X$ be a set. A $\textdef{permutation}$ of $X$ is a bijection from $X$ to $X$, so it's a function from $X$ into $X$ that is both one-to-one and onto. 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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