\begin{definition}[Definition:Line at Infinity]
Let $\LL$ be a straight line embedded in a cartesian plane $\CC$ given in homogeneous Cartesian coordinates by the equation:
:$l X + m Y + n Z = 0$
Let $l = m = 0$.
Then from Intersection of Straight Line in Homogeneous Cartesian Coordinates with Axes, $\LL$ intersects both the $x$-axis and the $y$-axis at the point at infinity.
Such a straight line cannot exist on $\CC$, so such an $\LL$ is known as the '''line at infinity'''.
\end{definition}