\begin{definition}[Definition:Axis/Z-Axis]
In a cartesian coordinate system, the '''$z$-axis''' is the axis passing through $x = 0, y = 0$ which is perpendicular to both the $x$-axis and the $y$-axis.
It consists of all the points in the real vector space in question (usually $\R^3$) at which all the elements of its coordinates but $z$ are zero.
As the visual field is effectively two-dimensional, it is not possible to depict a three-dimensional space on a visual presentation (paper, screen and so on) directly.
Therefore the representation of the third axis of such a cartesian coordinate system is necessarily a compromise.
However, if we consider the plane of the visual field as being a representation of the $x$-$y$ plane the '''$z$-axis''' can be ''imagined'' as coming "out of the page".
\end{definition}