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Definition: A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean space is given by the three-dimensional region satisfying x>0, -infinity<y<infinity, -infinity<z<infinity, while a half-plane is given by the two-dimensional region satisfying x>0, -infinity<y<infinity.