Ziegler in his lectures defines a cone as follows: a nonempty set of vectors $C \subset \mathbb{R}^d$ that with any finite set of vectors also contains all their linear combinations with nonnegative coefficients.
So is this saying that $C$ is just an arbitrary subset of $\mathbb{R}^d$ such that given any finite collection of points in $C$, any linear combination of these finitely many points with nonnegative coefficients is also in $C$? My main confusion is with "any finite set of vectors": is this finite set of vectors supposed to be a subset of $C$ or it can be any finite subset of $\mathbb{R}^d$?
I would appreciate any help. Thanks in advance.
