Generator of Cyclic Group/Examples/Subgroup of Multiplicative Group of Real Numbers Generated by 2

Example of Generators of Cyclic Group
Consider the multiplicative group of real numbers $\struct {\R_{\ne 0}, \times}$.

Consider the subgroup $\gen 2$ of $\struct {\R_{\ne 0}, \times}$ generated by $2$.

Then:
 * $\dfrac 1 2$ is also a generator of $\gen 2$

but:
 * $4$ is not a generator of $\gen 2$.