Definition:Multiplicative Group of Real Numbers

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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.