Points in general position I'm really confused by the definition of general position at wikipedia.
I understand that the set of points/vectors in $\mathbb R^d$  is in general position iff every $(d+1)$ points are not in any possible hyperplane of dimension $d$.
However I found that this definition is equivalent to affine independence (according to wiki). Does general linear position mean something else?
Could you please explain that? It is extremely confusing since a lot of people omit "linear" and so on.
Anyway could you also please give some hints on the way of proving general position? The hyperplane definition is hard to use.

Kundor's answer is correct, but I think this should be added for completeness.

Take a set of points $P \subset \mathbb R^d$. Then $P$ is in general linear position if and only if each k-tuple of points from $P$, $k=2,\dots,d+1$, is affinely independent.

But, as the OP notes, we only really need to check whether no $d+1$ points lie on a hyperplane of dimension $d$. This is equivalent with checking whether no $d+1$ points are affinely dependent.
