In
geometry, an
incidence relation is a
binary relation between different types of objects that captures the idea being expressed when phrases such as "a point
lies on a line" or "a line is
contained in a plane" are used. The most basic incidence relation is that between a point, , and a line, , sometimes denoted . If the pair is called a
flag. There are many expressions used in common language to describe incidence (for example, a line
passes through a point, a point
lies in a plane, etc.) but the term "incidence" is preferred because it does not have the additional connotations that these other terms have, and it can be used in a
symmetric manner, reflecting this property of the relation. Statements such as "line intersects line " are also statements about incidence relations, but in this case, it is because this is a shorthand way of saying that "there exists a point that is incident with both line and line ". When one type of object can be thought of as a set of the other type of object (
viz., a plane is a set of points) then an incidence relation may be viewed as
containment.