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**[SOLVED] rudin definition 3.16**

**1. Homework Statement**

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. Homework Equations**

**3. The Attempt at a Solution**

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