General Linear Position

A set of points in a $d$-dimensional Affine Space ($d$-dimensional Euclidean Space is a common example) is in general linear position (or just general position) if no $k$ of them lie in a $(k-2)$-dimensional flat for $k=2,3,...,d+1$. These conditions contain considerable redundancy since, if the condition holds for some value $k_0$ then it also must hold for all $k$ with $2\le k\le k_0$. Thus, for a set containing at least $d+1$ points in $d$-dimensional affine space to be in general position, it suffices that no Hyperplane contains more than $d$ points – i.e. the points do not satisfy any more linear relations than they must.