Definition:Ordered Tuple as Ordered Set/Ordered Tuple

Definition
The ordered tuple $\left({a_1, a_2, \ldots, a_n}\right)$ of elements $a_1, a_2, \ldots, a_n$ is defined as either the ordered pair:
 * $\left({a_1, \left({a_2, a_3, \ldots, a_n}\right)}\right)$

or as the ordered pair:
 * $\left({\left({a_1, a_2, \ldots, a_{n-1}}\right), a_n}\right)$

where $\left({a_2, a_3, \ldots, a_n}\right)$ and $\left({a_1, a_2, \ldots, a_{n-1}}\right)$ are themselves ordered tuples.

Whichever definition is chosen does not matter much, as long as it is understood which is used. And even then, the importance is limited.