Definition:Ordered Tuple as Ordered Set/Ordered Tuple

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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.

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