Definition:Additive Group of Rational Numbers
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Definition
The additive group of rational numbers $\struct {\Q, +}$ 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 $\struct {\Q, +}$ is $0$
- Each element of $\struct {\Q, +}$ has an inverse.