i am given a bounded function(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

y_n

[/itex]

by the law of bolzano Weierstrass

there has to be a sub sequence which converges.

[itex]

y_n_k

[/itex]

why ??

[itex]

lim sup y_n=>lim y_n_k

n-> infinity

[/itex]

lim sup is the supremum of the limits group of Xn

supremum is the least upper bound.so its bigger then any limit of a subsequence

correct?

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# Am i correct with bolzano Weierstrass lim inf/sup definition..

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