Hi there

I'm new here, but I guess I'm going to ask many questions in the future. I'm trying to study mathematics on my own, but I need some help to make sure I'm understanding the concepts correctly...

Anyways, here is my first problem. I'm reading some book and it is mentioned:

The concepts of union and intersection extend readily to large, possibly infinite, collections of sets. Suppose that "I" is some nonempty set (called an index set) and that for each i ∈ I we are given a set A_{i}... The union of this family of sets (denoted ) is the set of elements that are in at least one of the sets A_{i}, that is:

= {x|x ∈ A_{j}for some j ∈ I}

Where did the "j" come from???

I'm new to this kind of writing algebra and I guess my problem may be that I don't understand the "notation" perfectly. I mean, it's a bit vague. I think it is saying:

The union of this family of sets is equal to all the x members which belong to A_{j}and this "j" belongs to the set "I".

Now I don't understand; does this mean "the set of elements that are in at least one of the sets A_{i}"? And if yes, then what's the role of "j"? Where is the "at least" written?

I'll highly appreciate if you give me some general info about the union and intersection of such a family of sets and the way the notation is supposed to be read. I can't establish a connection from the notation to the book's statement in my mind.

This question may not belong here, but when I was searching the forum to find out if someone has asked the same question before, I noticed that almost all questions about sets are asked here.

Thanks a lot

Kindest Regards

Koohyar