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__Fact:__

Let a=lim sup a

_{n}.

Then for all ε>0, there exists N such that if n≥N, then a

_{n}<a+ε

============================

1) What is the "intuitive meaning" of this fact? I cannot seem to make sense of it...

2) Let a=lim sup a

_{n}.

Is it also true that:

For all ε>0, there exists N such that if n≥N, then

sup a

_{n}<a+ε ?

n≥N

Why or why not?

Thanks for explaining!

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