Definition:Half-Plane/Lower
Jump to navigation
Jump to search
Definition
Let $\PP$ be a Cartesian plane.
Let $\LL$ be the $x$-axis.
Open Lower Half-Plane
The open lower half-plane $\HH_{\text {OL} }$ is the area of $\PP$ below $\LL$.
That is, where $y < 0$:
- $\HH_{\text {OL} } := \set {\tuple {x, y}: y \in \R_{< 0} }$
Closed Lower Half-Plane
The closed lower half-plane $\HH_{\text {CL} }$ is the area of $\PP$ below and including $\LL$.
That is, where $y \le 0$:
- $\HH_{\text {CL} } := \set {\tuple {x, y}: y \in \R_{\le 0} }$