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A half-plane is a planar region consisting of all points on one side of an infinite straight line, and no points on the other side. If the points on the line are included, ...

The upper half-plane is the portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]>0 i.e., {x+iy:x in (-infty,infty),y in (0,infty)}. Common notations ...

The portion of the complex plane z=x+iy with real part R[z]<0.

The portion of the complex plane z=x+iy with real part R[z]>0.

The portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]<0, i.e., {x+iy:x in (-infty,infty),y in (-infty,0)}

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.

The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

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 ...