Simple maths question.

Well, that was embarrassing. I found the answer myself. N points span at most N-1 dimensions. Oops!

Cheers.

I believe it is the lesser of (n - 1) or m. In a 2 dimensional space (m = 2), if n = 2, you can define a line or curve, which is a one-dimensional (n - 1) manifold. If you have n = 3, you can define a plane, which is a two-dimensional manifold, e.g., maximum dimension of the manifold is m = (n - 1). If you have n > 3, all points lie in the same plane so you can't define more than a plane and max dimension doesn't go beyond m. For a 3 dimensional space, if n = 2, again manifold has dimension (n - 1), a 1-dimensional manifold. If n = 3, again a plane or a surface, a 2-dimensional manifold (n - 1), and if you have n = 4, now you can define a volume with dimension 3, m = (n - 1). Any more than 3 points, you're stuck with a volume of dimension m.