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?

Choose $n$, and note that $\cap_{k=1}^{n+1} A_k = A_{n+1}$, and $n \notin A_{n+1}$. Since $\cap_k A_k \subset A_{n+1}$, we see that $n \notin \cap_k A_k$. Hence $\cap_k A_k = \emptyset$.
