# Intersection of sets with infinite number of elements

1. Sep 10, 2011

### autre

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

If A1$\supseteq$A2$\supseteq$A3$\supseteq$...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!

2. Sep 10, 2011

### micromass

Just write it as

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

then

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

3. Sep 10, 2011

### 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)

4. Sep 11, 2011

### autre

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