1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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!!!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Indexed Collection of Sets ((
Loading...