Definition:Additive Group of Real Numbers

Definition
The additive group of real numbers $\left({\R, +}\right)$ is the set of real numbers under the operation of addition.

Also see

 * Real Numbers under Addition form Abelian Group

Thus real addition is:


 * Well-defined on $\R$
 * Closed on $\R$
 * Associative on $\R$
 * Commutative on $\R$
 * The identity of $\left({\R, +}\right)$ is $0$
 * Each element of $\left({\R, +}\right)$ has an inverse.