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

Infimun and supremum of empty set

  1. May 3, 2009 #1
    Why do we define(by convention) that infimum of an empty set as [tex]\infty[/tex] and supremum as [tex]-\infty[/tex]?
    Last edited: May 3, 2009
  2. jcsd
  3. May 3, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's not a convention -- it follows directly from the definition of the supremum as the least upper bound and the infimum as the greatest lower bound.
  4. May 3, 2009 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Remember that we say M is an upper bound for X if for all x in X.... so if X is the empty set then this is never true. Now, "false implies true is true", i.e. all possible real numbers are upper bounds for the the empty set.
  5. May 5, 2009 #4
    Thanks Hurkyl and matt grime for your replies. Yes I got it now!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Infimun and supremum of empty set