\begin{definition}[Definition:Ordered Tuple/Empty]
Let $S$ be a set.
The '''empty ordered tuple on $S$''' is the empty mapping:
:$\O \to S$
from the empty set $\O$ to $S$.
It is justified to call this an '''ordered tuple''' because the "first $0$ non-zero natural numbers" form the empty set:
:$\N^*_0 = \O$
\end{definition}