If $q \in \mathbb{Z}_+$, then for $a \in ]-1,1[$ is $$q < \frac{1}{a}$$
s.t.
$$a < \frac{1}{q}$$
The slight problem I see in this is that since $a$ can be positive or negative, then is the final inequality right? Since one switches it if one multiplies the first inequality by negative $a$. But not if one multiplies by positive $a$.
Do I need to take an absolute value somewhere? Because $a$ can take both positive and negative numbers.