Intersection of a Collection of Sets I am trying to figure out how to write out the answer to this.
If I am given: $$A_i = \{i,i+1,i+2,...\}$$
And I am trying to find the intersection of a collection of those sets given by:
$$\bigcap_{i=1}^\infty A_i $$
First off, am I right in saying its the nothing since:
$$A_1 = \{ 1,2,3,...\}$$
$$A_2 = \{ 2,3,4,...\}$$
So, would the answer be the empty set?

Yes, that's correct, the answer is the empty set.  To explain this properly you want to take a number $n \in \mathbb N$ and explain why $n \notin \bigcap A_i$.  If you do this with no conditions on $n$ you will have shown that the intersection doesn't contain any positive integers, hence it's empty.
To show $n \notin \bigcap A_i$ you must pick an $i$ such that $n \notin A_i$.  I leave it to you to determine which $i$ to pick.
