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!

Set notation (union and intersection)

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find simpler notation for the two sets:

    [tex]A= \bigcup^{\infty}_{j=0}[j,j+1][/tex]

    and

    [tex]B= \bigcap_{j \in Z}(R minus\ (j,j+1))[/tex]

    2. Relevant equations



    3. The attempt at a solution

    Not really sure what it means by "simpler notation"...

    Does [tex]A=R[/tex] since the union of [j,j+1] would eventually cover the whole interval?

    And [tex]B=Z[/tex] because the intersection of R minus (j,j+1) would only leave the integers because it is an open interval.
     
    Last edited: Oct 21, 2009
  2. jcsd
  3. Oct 21, 2009 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    For A you have the right idea, but is it really every single real number? Consider what the smallest element in A is.

    For B, it looks like each of the sets that you are taking the union of is

    R-(j,j+1)

    Shouldn't each of those sets be a subset of B then?
     
  4. Oct 21, 2009 #3
    Sorry, for B, it should be an intersection. I just fixed it.

    For A, I think it should be R+ since it starts at [0,1]..
     
  5. Oct 22, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    R+ sounds good, for B wirite it in terms of its complement and use the fact an intersection of complements is then complement of the union
     
  6. Oct 22, 2009 #5

    lanedance

    User Avatar
    Homework Helper

    re-read your first post - sounds about right for the 2nd one
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Set notation (union and intersection)
Loading...