Definition:Ordered Tuple/Defined by Sequence

Definition
Let $\left \langle {a_k} \right \rangle_{k \in A}$ be a finite sequence of $n$ terms.

Let $\sigma$ be a permutation of $A$.

Then the ordered $n$-tuple defined by the sequence $\left \langle {a_{\sigma \left({k}\right)}} \right \rangle_{k \in A}$ is the ordered $n$-tuple:
 * $\left \langle {a_{\sigma \left({\tau \left({j}\right)}\right)}}\right \rangle_{1 \le j \le n}$

where $\tau$ is the unique isomorphism from the totally ordered set $\left[{1 \,.\,.\, n}\right]$ onto the totally ordered set $A$.