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Prove that if $\{a_n\}$ is a sequence, then $\limsup a_n$ and $\liminf a_n$ are subsequential limits of $\{a_n\}$.

I don't know the case where $\limsup a_n = \infty$.

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    Same as for finite limsup.2012-10-20
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    Please don't write the whole question in the title. This is what the body is for.2012-10-20
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    We can actually define the limit superior and limit inferior of a sequence as the greatest and least limit point of the sequence, meaning they are subsequential limits of the sequence. With an alternate definition of them, you can prove they are indeed limit points and the if $x$ is any other limit point, it is between them.2013-01-11

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