Definition:Additive Group of Rational Numbers
Definition
The additive group of rational numbers $\left({\Q, +}\right)$ is the set of rational numbers under the operation of addition.
Also see
Thus rational addition is:
- Well-defined on $\Q$
- Closed on $\Q$
- Associative on $\Q$
- Commutative on $\Q$
- The identity of $\left({\Q, +}\right)$ is $0$
- Each element of $\left({\Q, +}\right)$ has an inverse.