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!

Determine Union of Sets Belonging to Interval

  1. Feb 3, 2014 #1
    Let ##I## denote the interval ## [0, \infty )## . For each r ## \in I ## define:

    ##A_{r} = \{ (x,y), \in ##R x R : ## x^{2} +y^{2} = r^{2} \}##
    ##B_{r} = \{ (x,y), \in ##R x R : ## x^{2} +y^{2} \leq r^{2} \}##
    ##C_{r} = \{ ## ... ## : ... > r^{2} \} ##

    a.) Determine ##\bigcup_{r\in I} A_{r} ## and ##\bigcap_{r \in I} A_{r}##

    For case, ##A_{3}##
    Is this right?
    For, ##A_{3} = \{ (3,0), (0,3), (\sqrt(4.5), \sqrt(4.5)) , (\sqrt(4.6), \sqrt(4.4)), \dots \}##

    Can I just list partitions of square roots that would give me 9?
     
    Last edited: Feb 3, 2014
  2. jcsd
  3. Feb 4, 2014 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, that is a partial list of elements in A3. Obviously there are infinitely many of them.

    For the purposes of solving the problem it would probably be instructive to think about what the set Ar is geometrically as well.
     
  4. Feb 4, 2014 #3
    Are they points that map the radius of a circle for ##A_{r}##?
     
  5. Feb 5, 2014 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That's a slightly odd way of saying it, but yes, Ar consists of the points of a circle of radius r, centred at the origin.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Determine Union of Sets Belonging to Interval
  1. Finding unions of sets (Replies: 3)

Loading...