Definition:Ordered Tuple as Ordered Set/Ordered Quadruple

Definition
The ordered quadruple $\tuple {a, b, c, d}$ of elements $a$, $b$, $c$ and $d$ is defined either as the ordered pair:
 * $\tuple {a, \tuple {b, c, d} }$

or:
 * $\tuple {\tuple {a, b, c}, d}$

where $\tuple {a, b, c}$ and $\tuple {b, c, d}$ are themselves ordered triples.

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