This notion is important in mathematics and its applications, because degenerate cases may require an exceptional treatment; for example, when stating exactly certain theorems and when writing computer programs.

The most frequent use is the following.

A set of points in the **d**-**dimensional** Euclidean space is said to be in **general position**, if no **d + 1** of them lie in a **(d-1)**-**dimensional** plane. Such set of points is also said to be **affinely independent**.

See the article about affine transformation for more.

If **d + 1** points are in a **(d-1)**-**dimensional** plane, it is called degenerate case or degenerate configuration.

In particular, a set of points in the plane are said to be in **general position**, if no three of them are on the same straight line. (Three points on a line is a degenerate case here).

In some contexts, e.g., when discussing Voronoi tesselations and Delaunay triangulations in the plane, the following definition is used.

A set of points in the plane are said to be in **general position**, if no three of them are neither on the same straight line nor on the same circle.

This definition can be generalized further: one may speak of points in general position with respect to a fixed class of algebraic relations (e.g. conic sections). In algebraic geometry this kind of condition is frequently met, in that points should impose *independent* conditions on curves passing through them.