Limits of sequences of subsets

1. Nov 2, 2011

spitz

1. The problem statement, all variables and given/known data

I'm just trying to find liminf and limsup for:

2. Relevant equations

$$E_n = (n, n+2)$$

3. The attempt at a solution

Since every subset occurs a finite number of times, would I say that limsup is the empty set? Is being bounded by nothing the same thing as being bounded by infinity?

For liminf:

$$((1,3)\cap(2,4)\cap...)\cup((2,4)\cap(3,5)\cap...)\cup...$$

I ended up with $$[2,∞)$$