Definition:Multiplicative Group of Real Numbers

Definition

The multiplicative group of real numbers $\struct {\R_{\ne 0}, \times}$ is the set of real numbers without zero under the operation of multiplication.

Also see

• Non-Zero Real Numbers under Multiplication form Abelian Group

Thus real multiplication is:

• Well-defined on $\R_{\ne 0}$
• Closed on $\R_{\ne 0}$
• Associative on $\R_{\ne 0}$
• Commutative on $\R_{\ne 0}$

and:

• The identity of $\struct {\R_{\ne 0}, \times}$ is $1$
• Each element of $\struct {\R_{\ne 0}, \times}$ has an inverse.

• Results about Multiplicative Group of Real Numbers can be found here.