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

Question about supremum and infimum

  1. Sep 30, 2012 #1
    Say we have [itex]a = \sup \{ a_{1}, a_{2}, a_{3}, ... \}[/itex]. Then does this mean we can find some [itex]a_{n} \in \{ a_{1}, a_{2}, ... \}[/itex] such that

    [tex]|a - a_{n}| < \varepsilon[/tex]

    ? My reasoning is that since a (the supremum) is the least upper bound of the set, we have to be able to find some member of the set that is arbitrarily close to a otherwise a wouldn't be a supremum anymore. Is this true?
     
    Last edited: Sep 30, 2012
  2. jcsd
  3. Sep 30, 2012 #2
    For any ε > 0 then yes, that's true.
     
  4. Oct 1, 2012 #3
    Well, if the the sup in the set iself then epsilon can indeed be zero.
    You may also find it interesting to think about finite sets.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about supremum and infimum
  1. Question about subset (Replies: 2)

Loading...