# Definition:Additive Group of Rational Numbers

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## 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.