My understanding of a basis $B$ of a vector space $V$ is, that it is a set of linearly independent vectors that spans the vector space.
Therefore, the 0 vector is not included in the basis,
and proper subset of the basis cannot span V.
And here comes my question. I am not quite sure what it meas for "another basis for V to be disjoint from B".
I understand that a basis is not unique, but for two distinct bases to be disjoint, does it mean that the intersection of the two bases is empty, or their span are disjoint ?