Definition:Half-Plane/Closed/Lower
< Definition:Half-Plane | Closed(Redirected from Definition:Closed Lower Half-Plane)
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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 $y \le 0$:
- $\HH_{\text {CL} } := \set {\tuple {x, y}: y \in \R_{\le 0} }$