Definition:Ordered Tuple/Also defined as

Ordered Tuple: Also defined as

Some treatments take the intuitive approach of regarding an ordered tuple merely as an ordered set, that is, without stressing the fact of it being a mapping from a subset of the natural numbers:

Ordered Tuple as Ordered Set

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.