Definition:Ordered Tuple as Ordered Set/Ordered Quadruple

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

or:
 * $\left({\left({a, b, c}\right), d}\right)$

where $\left({a, b, c}\right)$ and $\left({b, c, d}\right)$ 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.