if $\displaystyle \Omega_n:=\{ z\in \mathbb{C} : z^n=1 \}

$ , then it's a cyclic group with an order n, and one generator $\displaystyle (cis\frac{2\pi}{n})$.

Does $\displaystyle \Omega_\infty$ have a finite number of generators? (How do you prove \ disproof this?)