Geometry of Space/Plane Question?

Question

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Which inequality describes the half-space of the set of points below the xy-plane

Answer 1

If we're in 3-dimensional space described by points (x,y,z).

We can then describe the open half-space of points "below" the xy-plane as all points (x,y,z) where z<0.  Despite lacking proper notation we define a set S,describing this half space, as such:

S = {(x,y,z) : x is any real number, y is any real number, z is any real number less than 0}  

In the case of a close half-space z ≤ 0.