Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Set operation

  1. Jul 20, 2010 #1
    Hello all,


    I have the following question regarding the interchange between union and intersection.

    [tex] \cup_{q < t} \cap_{s > q} A_{s} = \cap_{s<t} \cup_{q<s} A_{q} = \cup_{q < t} A_{q}[/tex]

    Am I correct? Also, can anyone provide me some more resources regarding this kind of interchange in set operation or change of variable technique?

    Thanks.


    Wayne
     
  2. jcsd
  3. Jul 20, 2010 #2
    Off the top of my head, it doesn't look correct.

    Suppose Ai is empty for all i>100. Then [tex]\cap_{s>q}A_s[/tex] will be empty for all q, and the union of these will be empty. So lhs is empty.

    But rhs, being just a union of As, will not necessarily be empty.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook