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