In algebraic geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible. Its precise meaning differs in different settings.
For example, generically, two lines in the plane intersect in a single point (they are not parallel or coincident). One also says "two generic lines intersect in a point", which is formalized by the notion of a generic point. Similarly, three generic points in the plane are not colinear – if three points are collinear (even stronger, if two coincide), this is a degenerate case.
This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating general theorems or giving precise statements thereof, and when writing computer programs (see generic complexity).
Read more about General Position: General Linear Position, More Generally, Different Geometries, General Type, Other Contexts, Abstractly: Configuration Spaces
Famous quotes containing the words general and/or position:
“The most general deficiency in our sort of culture and education is gradually dawning on me: no one learns, no one strives towards, no one teaches—enduring loneliness.”
—Friedrich Nietzsche (1844–1900)
“To place oneself in the position of God is painful: being God is equivalent to being tortured. For being God means that one is in harmony with all that is, including the worst. The existence of the worst evils is unimaginable unless God willed them.”
—Georges Bataille (1897–1962)