# Definition:Half-Plane/Open/Left

## Definition

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 $x < 0$:

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