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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
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