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Homework Help: Indexed Collection of Sets ((

  1. Sep 10, 2008 #1
    Indexed Collection of Sets ... :(((

    My notes are confusing me so bad, worst part is that we're not using our book till later on and that just kills me a lot. I'm very text-book because notes never make sense to me.

    Let [tex]A_n=[0,n][/tex]

    a) What numbers are in [tex]\bigcup_{n=1}^{\infty}A_n[/tex]?

    b) What numbers are in [tex]\bigcap_{n=1}^{\infty}A_n[/tex]?

    Ok, so I have an example here ...

    If

    [tex]I=\{1,2,3...\}[/tex]

    [tex]A_i=[-i,i][/tex]

    Then

    [tex]\bigcup=\mathbb{R}[/tex]

    [tex]\bigcap=[-1,1][/tex]

    I honestly, can't remember how we got [-1,1]???

    a) Since An goes from 0 to n, wouldn't that make [tex]\bigcup=[0,\infty)[/tex]???
     
  2. jcsd
  3. Sep 10, 2008 #2

    Dick

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    Re: Indexed Collection of Sets ... :(((

    Sure. The union is [0,infinity). What's the intersection? In your example, the intersection is [-1,1] because the smallest index is 1. I'm not sure what's confusing you so seriously here? Draw a picture of the sets.
     
  4. Sep 10, 2008 #3
    Re: Indexed Collection of Sets ... :(((

    Wouldn't my intersection for my example also be all real numbers? I could choose the smallest index within my set, which is 1. But I could continue choosing within the real number system, giving me an infinite amount of options.

    [tex]\bigcap=\mathbb{R}[/tex]???
     
  5. Sep 10, 2008 #4

    Dick

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    Re: Indexed Collection of Sets ... :(((

    No, no, no. The smallest set in your system is A_1 All of the others include it. An element of the intersection has to be in ALL of the sets. The intersection is [0,1].
     
  6. Sep 10, 2008 #5
    Re: Indexed Collection of Sets ... :(((

    OHHH!!! In ALL the sets, makes a lot of sense now.

    Because once I move onto n=2, I would have 0, 1, 2, but going back to n=1, it doesn't contain 2.

    YAYYY :) Thanks!!!
     
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