# Index set and unions

## 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.

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

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
Staff Emeritus