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

1. transgalactic

i am given a bounded function
$y_n$
by the law of bolzano Weierstrass
there has to be a sub sequence which converges.
$y_n_k$

why ??
$lim sup y_n=>lim y_n_k n-> infinity$

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?