Hello everybody,

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

I have sets for all . 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. However, If I said: 1 > 0 what is obviously true I could divide by any positive n to get: 1/n > 0 and any negative -n to get -1/n < 0. Consequently 0 would be in this intersection but I'm not sure at all... Thank you for any help!

Best, Rafael