Originally Posted by

**raphw** Hello everybody,

I was wondering if this infinite intersections of sets was empty.

I have sets $\displaystyle (-\frac{1}{n},\frac{1}{n})$ for $\displaystyle n \in N$. I was wondering if 0 was in the set of the intersection of all these subsets. I can prove that all negative or positive numbers are not, using the Archimedian property of R. However, this does not work for the number zero so I am puzzled if this was an element of the intersection. Intuitvely I would say no but I cannot prove it. Thank you for any help!

Best, Rafael