Definition:Half-Plane/Left
< Definition:Half-Plane(Redirected from Definition:Left Half-Plane)
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Definition
Let $\PP$ be a Cartesian plane.
Let $\LL$ be the $y$-axis.
Open Left Half-Plane
The open left half-plane $\HH_{\text {OL} }$ is the area of $\PP$ on the left of $\LL$.
That is, where $x < 0$:
- $\HH_{\text {OL} } := \set {\tuple {x, y}: x \in \R_{<0} }$
Closed Left Half-Plane
The closed left half-plane $\HH_{\text {CL} }$ is the area of $\PP$ on the left of and including $\LL$.
That is, where $x \le 0$:
- $\HH_{\text {CL} } := \set {\tuple {x, y}: x \in \R_{\le 0} }$