Definition:Ordered Tuple as Ordered Set

Definition
The rigorous definition of an ordered tuple is as a sequence whose domain is $\N^*_n$.

However, it is possible to treat an ordered tuple as an extension of the concept of an ordered pair.

Ordered Triple
The ordered triple $\left({a, b, c}\right)$ of elements $a$, $b$ and $c$ is defined as the ordered pair:
 * $\left({a, \left({b, c}\right)}\right)$

where $\left({b, c}\right)$ is itself an ordered pair.

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

where $\left({b, c, d}\right)$ is itself an ordered triple.

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

where $\left({a_2, a_3, \ldots, a_n}\right)$ is itself an ordered tuple.

Alternative definition
Some sources define the ordered tuple $\left({a_1, a_2, \ldots, a_n}\right)$ of elements $a_1, a_2, \ldots, a_n$ as the ordered pair:
 * $\left({\left({a_1, a_2, \ldots, a_{n-1}}\right), a_n}\right)$

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

Also see

 * Equality of Ordered Tuples