\begin{definition}[Definition:Half-Plane/Open/Left]
Let $\PP$ be a Cartesian plane.
Let $\LL$ be the $y$-axis.
The '''open left half-plane''' $\HH_{\text {OL} }$ is the area of $\PP$ on the left of $\LL$.
That is, where $x < 0$:
:$\HH_{\text {OL} } := \set {\tuple {x, y}: x \in \R_{<0} }$
\end{definition}