I came across this statement while I was reading some topic: we have a sequence $\{ a_n \}$ of real numbers, such that $|f(x)|\geq \frac{1}{a_n}$ for all $n\in \mathbb Z$, then
" if $\inf a_{n}=a>0$, then $\sup |f(x)| \geq \frac{1}{a} $"
How can the above conclusion be true?
As I know since $\inf a_{n}=a$ then $a_n \geq a$ for all $n$, and $\frac{1}{a_n} \leq \frac{1}{a} $!!
Thanks