intersection of $(-1/n,1/n)$ as n$ \to \infty$ , is it empty?

What is the intersection of the set $(-1/n, 1/n)$ as $n \to \infty$?

I got this idea of intersection from Intersection of open sets?, shouldnt the intersection be the empty set since a number cannot be any number since it must be both a positive and negative real number.. Some say zero is the intersection but zero is not positive nor negative, sorry for not being clear