The counterpart to subspaces are "quotient vector spaces". Given any subspace , the quotient space "V"/"W" (""V" modulo "W"") is defined as follows: as a set, it consists of where v is an arbitrary vector in "V". The sum of two such elements and is and scalar multiplication is given by . The key point in this definition is that if and only if the difference of v1 and v2 lies in "W". This way, the quotient space "forgets" information that is contained in the subspace "W".