However, the set of all nonzero rational numbers Q ∖ ∖ { 0 } = { q ∈ ∈ Q ∣ ∣ q ≠ ≠ 0 } does form an abelian group under multiplication, also denoted ⁠ Q × × ⁠. Associativity and identity element axioms follow from the properties of integers. The closure requirement still holds true after removing zero, because the product of two nonzero rationals is never zero. Finally, the inverse of a / b is ⁠ b / a ⁠, therefore the axiom of the inverse element is satisfied.