Definition:Ordered Tuple as Ordered Set/Ordered Tuple

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

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

where $\tuple {a_2, a_3, \ldots, a_n}$ and $\tuple {a_1, a_2, \ldots, a_{n - 1} }$ 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.