A spanning set of a vector space 
is a set 
of vectors whose vector
space span is 
. Equivalently, every vector
in 
is a finite linear combination of elements of 
.
The finiteness applies to each linear combination,
even when 
is an infinite set.
A spanning set need not be linearly independent. For example, 
spans 
, but its third vector
is the sum of the first two. A spanning set that is linearly
independent is a vector basis. Every finite
spanning set contains a vector basis, obtained by
removing redundant vectors.
