\begin{definition}[Definition:Permutation on n Letters]
Let $\N_k$ be used to denote the initial segment of natural numbers:
:$\N_k = \closedint 1 k = \set {1, 2, 3, \ldots, k}$
A '''permutation on $n$ letters''' is a '''permutation''':
:$\pi: \N_n \to \N_n$
The usual symbols for denoting a general '''permutation''' are $\pi$ (not to be confused with the famous circumference over diameter), $\rho$ and $\sigma$.
\end{definition}