\begin{definition}[Definition:Point at Infinity]
Let $\LL_1$ and $\LL_2$ be straight lines embedded in a cartesian plane $\CC$, given by the equations:
{{begin-eqn}}
{{eqn | lll = \LL_1:
      | l = l_1 x + m_1 y + n_1
      | r = 0
}}
{{eqn | lll = \LL_2:
      | l = l_2 x + m_2 y + n_2
      | r = 0
}}
{{end-eqn}}
Let $l_1 m_2 = l_2 m_1$, thus by Condition for Straight Lines in Plane to be Parallel making $\LL_1$ and $\LL_2$ parallel.
In this case the point of intersection of $\LL_1$ and $\LL_2$ does not exist.
However, it is convenient to define a '''point at infinity''' at which such a pair of parallel lines hypothetically "intersect".
\end{definition}