My proof class just took a turn for the worst for me - I don't understand this. First, the notation is extremely confusing to me, I need help to make sure I'm getting this. If An is some set for some natural number n such as [-n, n]. Then (script A) the collection is the set of all An? Is that correct? Just a basis needed.. Now, the definitions of unions and intersections got me super confused. But what I am getting out of it.. is that U(script A) Is the set of all x that are in any of the An in the collection, while (intersection) An is the set of all x that are in every An in the collection? So, in my example, U(script A) is the set of all x that are in at least one of the An, which is all real numbers, because all real numbers will fall into one of those intervals. while (intersection)(script A) is the set of all x that are in all An, which is the empty set, because no real number will fall into every one of those intervals. Ugh.. does anyone even know what I'm talking about? This is strange.