I have trouble understanding something in a book I am reading.
It says for the following:
$c_1\leq \frac{1}{2} - \frac{3}{n}\leq c_2$ where $c_1,c_2$ are positive constants, $n$ is a positive variable.
It says that
We can make the right-hand inequality hold for any value of $n \geq 1$ by choosing any constant $c_2 \geq \frac{1}{2}$.
But if I start to work with the right hand side, I end up with $c_2\lt\frac{1}{2}$.
Does the book have a typo or am I wrong?
I also have different result for the left-hand side inequality but I leave it out.
UPDATE (after comments):
$\begin{align*} \frac{1}{2}-\frac{3}{n}\leq c_2 &\Longleftrightarrow \frac{n}{2}-3 \leq nc_2\\ &\Longleftrightarrow \frac{n}{2}-nc_2 \leq 3\\ &\Longleftrightarrow n\left(\frac{1}{2}-c_2\right)\leq 3\\ &\Longleftrightarrow n\leq \frac{3}{\frac{1}{2}-c_2}\\ \end{align*}$ So it must be $\frac{1}{2}-c_2 \gt 0$, so $c_2 \lt \frac{1}{2}$ (I think)