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