How would I show that a group of positve rational numbers under multiplication is not cyclic.
I can see that its true, but how would I prove it
Suppose it is. Let $\displaystyle x$ be the generator. If $\displaystyle x$ is an integer then $\displaystyle x^n$ is an integer which means it cannot generate the non-integers. If $\displaystyle x$ is a non-integer then $\displaystyle x^n$ is a non-integer which means it cannot generate the integers.