Intersection of an infinite set

[michonamona]

Let $$G_{n}$$ = (-1/n,1/n) for all n in N

let $$G= \bigcap^{\inft}_{n=1}$$

 

[irycio]

So, what's the question/problem?? The intersection is simply 0 (zero, a single number). Hence the intersection of an infinite number of open sets is not necessarily open, whereas the union is always open, as is the finite intersectiion of them. With the closed sets, it's the other way round :).