# Definition:Half-Plane/Open/Lower

## Definition

Let $\PP$ be a Cartesian plane.

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

The open lower half-plane $\HH_{\text {OL} }$ is the area of $\PP$ below $\LL$.

That is, where $y < 0$:

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