Why does this lemma hold true in this paper?

Question

Here is paper on arXiv.

See Lemma 2：

$$ |W(s)| = \left|\frac{\zeta(s)}{\zeta(1-s)}\right| \ne 1 $$ leads to $$ |\zeta(s)| \ne |\zeta(1-s)|$$ when $$|W(s)| > 0$$

But how does it hold true?

Answer 1

If $\frac ab \ne 1$ then $a\ne b$. You should be able to prove that.[1].

And $|\frac cd| =\frac {|c|}{|d|}$. You should be able to prove that. [2].

So if $|\frac ab| =\frac {|a|}{|b|} \ne 1$ then $|a| \ne |b|$.

That's all.

By the way. If $|W(s)| = 0$ then $\left|\frac {\zeta(s)}{\zeta(1-s)} \right| = 0$ and $\zeta(s) = 0$ but $\zeta(1-x) $ can not be $0$ or that fraction would be undefined.