How to show that
$\limsup \{a_n\}=-\liminf \{-a_n\}$
I could use this property : if $a= \sup(X) $ then, $-a=\inf(-X)$?
where
$\lim\sup\{a_n\}=\lim_{n\rightarrow\infty}[\sup\{a_k\,|\,k\geq n\}]$
$\liminf\{a_n\}=\lim_{n\rightarrow\infty}[\inf\{a_k\,|\,k\geq n\}]$
