# Definition:Half-Plane/Closed/Left

## Definition

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 $x \le 0$:

$\HH_{\text {CL} } := \set {\tuple {x, y}: x \in \R_{\le 0} }$