Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a projective line is a one-dimensional projective space. The projective line over a field K, denoted P1(K), may be defined as the set of one-dimensional subspaces of the two-dimensional vector space K2 (it does carry other geometric structures). For the generalisation to the projective line over an associative ring, see inversive ring geometry. The projective line over the real numbers is called the real projective line. It may also be thought of as the line K together with an idealised point at infinity ; the point connects to both ends of K creating a closed loop or topological circle. An example is obtained by projecting points in R2 onto the unit circle and then identifying diametrically opposite points. In terms of group theory we can take the quotient by the subgroup {1,–1}. Compare the extended real number line, which distinguishes and – .

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