Definition:Additive Group of Rational Numbers

Definition
The additive group of rational numbers $\struct {\Q, +}$ is the set of rational numbers under the operation of addition.

Also see

 * Rational Numbers under Addition form Infinite Abelian Group

Thus rational addition is:


 * Well-defined on $\Q$
 * Closed on $\Q$
 * Associative on $\Q$
 * Commutative on $\Q$
 * The identity of $\struct {\Q, +}$ is $0$
 * Each element of $\struct {\Q, +}$ has an inverse.