i look every where for that basic proof

that if

lim inf An=lim sup An then the sequence converges

??

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- December 13th 2008, 02:08 AMtransgalactici cant find the basic lim inf=lim sup convergence proof
i look every where for that basic proof

that if

lim inf An=lim sup An then the sequence converges

?? - December 13th 2008, 02:32 AMMoo
- December 13th 2008, 02:39 AMtransgalactic
i have to proove this definition

- December 13th 2008, 09:39 AMMathstud28
Let be the set of all subsequential limits of . Also let . So it is clear that if then . Now let us define a subsequence of as where and is strictly increasing. So since it is clear that there exists a such that .Now based on the above definition we may say that as soon as which says exactly that not only does converge, but it converges to .

That is how I would do it. Is that acceptable?

You may find this thread helpful http://www.mathhelpforum.com/math-he...-analysis.html - December 14th 2008, 01:42 AMJhevon
- December 14th 2008, 09:09 AMMathstud28
No I don't where is the set of all subsequential limits. The same goes for

Quote:

secondly, your proof suggests that the sequence is constant, which of course, is not true for convergent sequences in general.

- December 14th 2008, 01:39 PMJhevon