Definition:Additive Group of Real Numbers
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Definition
The additive group of real numbers $\struct {\R, +}$ is the set of real numbers under the operation of addition.
Also see
Thus real addition is:
- Well-defined on $\R$
- Closed on $\R$
- Associative on $\R$
- Commutative on $\R$
- The identity of $\struct {\R, +}$ is $0$
- Each element of $\struct {\R, +}$ has an inverse.
- Results about the additive group of real numbers can be found here.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 4.5$. Examples of groups: Example $81$