1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Rudin definition 3.16

  1. Mar 16, 2008 #1
    [SOLVED] rudin definition 3.16

    1. The problem statement, all variables and given/known data
    This question refers to Rudin's Principles of Mathematical Analysis.

    Why does Rudin not just define s* as the supremum of the sequence {s_n} instead of the supremum of the set E. Isn't that equivalent and also much simpler?
    Also it seems like Rudin assumes that the lim sup exists for every sequence. I do not see why the set E has to be nonempty.

    EDIT: never mind; it is not hard to show that E will ALWAYS be nonempty and that the sup of a sequence is not necessarily the same as its lim sup
    2. Relevant equations

    3. The attempt at a solution
    Last edited: Mar 16, 2008
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted