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- Thread starter zzzhhh
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mathman

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I cannot understand your reply, could you please explain in more detail? Thanks.

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mathman

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My original intention is to try to establish the statement "both lim sup f(x) and lim inf f(x) exist and equal c (possibly [tex]\pm\infty[/tex]) iff lim f(x) exists and equals c" from analogical statement for sequence. But now this approach is not feasible. I then proved the above statement for functions by definition. Thank you again, mathman!

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Office_Shredder

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It is well known that limit of function can be converted to limit of sequenc

This is only true for functions that are continuous at the point. So it's not surprising that a limsup styled in the same manner would fail for a function that is everywhere discontinuous

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