Intersection of sets with infinite number of elements

[autre]

I have to decide whether the following is true or false:

If A1\supseteqA2\supseteqA3\supseteq...are all sets containing an infinite number of elements, then the intersection of those sets is infinite as well.

I think I found a counterexample but I'm not sure the correct notation. I to have sets {n, n+1, n+2,...} from n to infinity (so {1, 2, 3,...}\supseteq{2,3,4,...}) and the intersection of those sets is obviously null. How do I write this out? Thanks!

 

[micromass]

Just write it as

A_n=\{n,n+1,n+2,...\}

then

\bigcap_{n\in \mathbb{N}}{A_n}=\emptyset

 

[disregardthat]

The intersection of a set of sets is the set of elements contained in every of those sets. What number is contained in every such set? (Hint: assume n is in the intersection, and find a set which does not contain n)

 

[autre]

Thanks micromass, that's the notation I was looking for.