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Let a=lim sup a_{n}.

Then for all ε>0, there exists N such that if n≥N, then a_{n}<a+ε

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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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# Limit superior (lim sup) of a sequence

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