 When the sequence contains no vectors or only one vector, the original definition is used.In order to allow the number of linearly independent vectors in a vector space to be countably infinite, it is useful to define linear dependence as follows.More generally, let "V" be a vector space over a field "K", and let {"v""i" | "i" ∈ "I"} be a family of elements of "V" indexed by the set "I".