Understanding Index Sets and Unions in Set Theory: Real Analysis Explained

[Chantry]

Homework Statement

I'm reading through the introductory pages of my real analysis book and for some reason I can't wrap my head around this seemingly simple concept. The book is talking about collections of sets and something new to me called the "index set".

I apologize ahead of time, because I don't know how to properly format my formulas.

Let U be the union and ^ be the intersection.

U from n = 1 to infinite of (0,n) = (0,infinite)
^ from n = 1 to infinite of (0,n) = (0,1)

I have no idea what that is supposed to represent.

Another example,

U n = 1 to infinite of (-n,n) = R
^ n = 1 to infinite (-n,n) = (-1,1)

I don't understand where that logical jump comes from. What does the integers have to do with the Reals? and -1,1? I'm completely at a loss to explain what they're trying to get across.

I think I'm missing something vital here, but I think the book is skimming over the subject as it's probably pretty elementary. Can anyone help me fill in the gap?

Homework Equations

There's not really anything to say here. It's basic set theory.

The Attempt at a Solution

It's a simple matter of notation and it's not in the form of a question, so this isn't applicable for my question.

 

[vela]

Are you missing the fact that (a,b) is the interval consisting of all real numbers x such that a<x<b?

 

[Chantry]

Definitely missed that completely.

Thanks a lot. It's amazing how the simplest things can sometimes give you so much trouble.

Just to make sure I'm understanding it correctly, the U 1 to infinite of (0,n) is saying you're doing a union of {0, .. Real Values, .., 1} U {0, .., 2} U {0,..,3} .. U {0,..,infinite}, correct?

 

[vela]

Yup.