\begin{definition}[Definition:Ordered Tuple/Defined by Sequence]
Let $\sequence {a_k}_{k \mathop \in A}$ be a finite sequence of $n$ terms.
Let $\sigma$ be a permutation of $A$.
Then the '''ordered $n$-tuple defined by the sequence $\sequence {a_{\map \sigma k} }_{k \mathop \in A}$''' is the ordered $n$-tuple:
:$\sequence {a_{\map \sigma {\map \tau j} } }_{1 \mathop \le j \mathop \le n}$
where $\tau$ is the unique isomorphism from the totally ordered set $\closedint 1 n$ onto the totally ordered set $A$.
{{WIP|page proving existence and uniqueness of isomorphism}}
\end{definition}