# Definition:Half-Plane/Open/Upper

## Definition

Let $\PP$ be a Cartesian plane.

Let $\LL$ be the $x$-axis.

The open upper half-plane $\HH_{\text {OU} }$ is the area of $\PP$ above $\LL$.

That is, where $y > 0$:

$\HH_{\text {OU} } := \set {\tuple {x, y}: y \in \R_{> 0} }$