Half Space

in mathematics, the set of points in space that lie on one side of some plane. The coordinates x, y, and z of the points of a half space satisfy the inequality Ax + By + Cz + D > 0, where A, B, C, and D are constants such that A, B, and C are not simultaneously equal to zero. The plane Ax + By + Cz + D = 0 is called the boundary of the half space. If the boundary is included in the half space, the half space is said to be closed.