Understanding Math Notation: Unions and Intersections Explained

[Oddbio]

In my math book, I am seeing a few things like this:

For any set I, and any family $(A_{i})_{i\in I}$ of open subsets, the union $\cup_{i\in I}A_{i}$ is also an open set (any union of open sets is open);

I also see one later like:
$$\cap^{n}_{i=1}A_{i}$$

But I always thought that a union (and intersection) had to be of the form:
$$A\cup B or A\cap B$$

So the first one has nothing on the left side, same as the second one.. but the second one also has super and sub-scripts?
Do they mean something completely different than "union" and "intersection"?

I apologize if this is a trivial question.. it sure feels like it.

 

[nicksauce]

The notation of the form $\cup_{i\in I}A_{i}$, means that you have a family of sets A_i, and you do the union of all of them. i.e.,

$$\cup_{i\in I}A_{i} = A_1\cup A_2\cup...$$

 

[nicksauce]

Actually I guess that isn't strictly true, since the family of sets doesn't have to be countable, but I hope you get the idea.