# Definition:Half-Plane/Closed/Lower

## Definition

Let $\PP$ be a Cartesian plane.

Let $\LL$ be the $x$-axis.

The closed lower half-plane $\HH_{\text {CL} }$ is the area of $\PP$ below and including $\LL$.

That is, where $y \le 0$:

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