[tex](adsbygoogle = window.adsbygoogle || []).push({});

\liminf _{n->\infty} x_n+\limsup _{n->\infty} y_n\leq \limsup _{n->\infty} (x_n+y_n)\leq\limsup _{n->\infty} x_n+\limsup _{n->\infty} y_n\\

[/tex]

proving the first part:

[tex]

\limsup _{n->\infty} (x_n+y_n)\leq\limsup _{n->\infty} x_n+\limsup _{n->\infty} y_n\\

[/tex]

lim sup is the supremum of all the limits of the subsequences

this is true because of some law regarding the sum of two subsequences

correct??

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# Lim inf/sup innequality question

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