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

The intersection of an empty collection of subsets of X is equal to X?

  1. Jul 29, 2009 #1
    Hi,

    I'm reading HL Royden's real analysis, though my question pertains more to set theory.

    Let X be a set. Then the intersection of an empty collection of subsets of X is equal to X. I understand this is not an intersection of empty subsets but it is still very counter-intuitive. Can anyone provide insight?
     
  2. jcsd
  3. Jul 29, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, what element wouldn't be in the intersection?
     
  4. Jul 29, 2009 #3
    Consider an intersection of lots of sets. If you take fewer sets, the intersection is bigger, right? So, in the ultimate case, when you take the fewest sets of all, the intersection is as big as possible.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: The intersection of an empty collection of subsets of X is equal to X?
  1. Var[X+Y] equality true (Replies: 6)

Loading...