Definition:Half-Plane/Right
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Definition
Let $\PP$ be a Cartesian plane.
Let $\LL$ be the $y$-axis.
Open Right Half-Plane
The open right half-plane $\HH_{\text {OR} }$ is the area of $\PP$ on the right of $\LL$.
That is, where $x > 0$:
- $\HH_{\text {OR} } := \set {\tuple {x, y}: x \in \R_{>0} }$
Closed Right Half-Plane
The closed right half-plane $\HH_{\text {CR} }$ is the area of $\PP$ on the right of and including $\LL$.
That is, where $x \ge 0$:
- $\HH_{\text {CR} } := \set {\tuple {x, y}: x \in \R_{\ge 0} }$