Check my understanding of vector spaces
So I just started learning linear algebra on my own very recently, right now Im learning about vector spaces and just wanted a sanity check of what vector spaces are. To my understanding, a vector space is a collection of objects called vectors, and vectors in this context are essentially anything that we can scale by a constant and add together (they must also follow 8 other axioms related to this but that's the gist). And all possible linear combinations of these vectors must remain within this defined space. Is this a correct understanding (or at least approximately)? My other question is what exactly is meant by all combinations of the vectors must remain within this space, like I understand it intuitively but how do we define the boundaries of this space or is the boundaries of this space described by the combinations of the vectors within it?