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

  1. i am given a bounded function
    [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?
     
  2. jcsd
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