Vector space
There are some combinations of vectors that are special. A minimum set of vectors that—through some combination of addition and multiplication—can reach any point in the vector space is called a basis (of that vector space). It is true that every vector space has a basis. It is also true that all bases of any one vector space have the same number of vectors in them. This is called the dimension theorem. We can then define the dimension of a vector space to be the size of its basis.