Definition:Half-Plane/Open/Lower
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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 $y < 0$:
- $\HH_{\text {OL} } := \set {\tuple {x, y}: y \in \R_{< 0} }$