Empty set

• What Is the Cartesian Product with the Empty Set?
  The Cartesian product of any set with the empty set is empty: neither A × ∅ nor ∅ × A contains an ordered pair.
• What Does It Mean for a Set Not to Contain the Empty Set?
  A set that does not contain the empty set satisfies ∅ ∉ A; this differs from being nonempty and from the fact that ∅ is a subset of every set.