# 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

Thus real multiplication is:

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.