Definition:Additive Group of Real Numbers

Definition

The additive group of real numbers $\struct {\R, +}$ is the set of real numbers under the operation of addition.

Also see

• Real Numbers under Addition form Infinite Abelian Group

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 $81$