text: If V is a vector space, one distinguishes "vector hyperplanes" (which are linear subspaces, and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by translation of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two half spaces, and defines a reflection that fixes the hyperplane and interchanges those two half spaces.
  Special types of hyperplanes
  Several specific types of hyperplanes are defined with properties that are well suited for particular purposes. Some of these specializations are described here.
  Affine hyperplanes
  An affine hyperplane is  an affine subspace of codimension 1 in an affine space.
  In Cartesian coordinates, such a hyperplane can be described with a single linear equation of the following form (where at least one of the s is non-zero and  is an arbitrary constant):
  In the case of a real affine space, in other words when the coordinates are real numbers, this affine space separates the space into two half-spaces, which are the connected components of the complement of the hyperplane, and are given by the inequalities
  and
  As an example, a point is a hyperplane in 1-dimensional space, a line is a hyperplane in 2-dimensional space, and a plane is a hyperplane in 3-dimensional space. A line in 3-dimensional space is not a hyperplane, and does not separate the space into two parts (the complement of such a line is connected).