\begin{definition}[Definition:Permutation on n Letters/Set of Permutations]
Let $\N_k$ be used to denote the (one-based) initial segment of natural numbers:
:$\N_k = \closedint 1 k = \set {1, 2, 3, \ldots, k}$
The '''set of permutations of $\N_n$''' is denoted $S_n$.
\end{definition}