\begin{definition}[Definition:Coordinate System/Origin]
The '''origin''' of a coordinate system is the zero vector.
In the $x y$-plane, it is the point:
:$O = \tuple {0, 0}$
and in general, in the Euclidean space $\R^n$:
:$O = \underbrace {\tuple {0, 0, \ldots, 0} }_{\text{$n$ coordinates} }$
Thus it is the point where the axes cross over each other.
\end{definition}