Rudin definition 3.16

1. Mar 16, 2008

ehrenfest

[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