Editing Finite geometry (section)

===Classification of finite projective spaces by geometric dimension===
*Dimension 0 (no lines):  The space is a single point and is so degenerate that it is usually ignored.
*Dimension 1 (exactly one line):  All points lie on the unique line, called a ''projective line''.
*Dimension 2:  There are at least 2 lines, and any two lines meet.  A projective space for {{nowrap|1=''n'' = 2}} is a [[projective plane]].  These are much harder to classify, as not all of them are isomorphic with a {{nowrap|PG(''d'', ''q'')}}.  The [[Desarguesian plane]]s (those that are isomorphic with a {{nowrap|PG(2, ''q'')}}) satisfy [[Desargues's theorem]] and are projective planes over finite fields, but there are many [[non-Desarguesian plane]]s.
*Dimension at least 3:  Two non-intersecting lines exist.  The [[Veblen–Young theorem]] states in the finite case that every projective space of geometric dimension {{nowrap|''n'' ≥ 3}} is isomorphic with a {{nowrap|PG(''n'', ''q'')}}, the ''n''-dimensional projective space over some finite field GF(''q'').