- Given a vector space V and a subspace W of V.
- "x≡y (mod W) if x-y∈W" defines equivalence relation.
- equivalence relation partitions V into equivalence classes.
- equivalence classes is called cosets of W in V.
- Define the quotient space V/W, whose elements are cosets of W in V.
If x & y ∈ W, x-y∈W. So it seems W⊆quotient space since W is a coset of itself. True? If yes, why V/W?