\begin{definition}[Definition:Derangement]
A '''derangement''' is a permutation $f: S \to S$ from a set $S$ to itself where $\map f s \ne s$ for any $s \in S$. 
If $S$ is finite, the number of '''derangements''' is denoted by $D_n$ where $n = \card S$ (the cardinality of $S$.)
\end{definition}