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.