- #1
filter54321
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Homework Statement
Show that the lim sup of a bounded sequence is a limit of a subsequence.
Homework Equations
Sequence: Sn
Subsequence: Snk
The Attempt at a Solution
An existent lim sup means that at a large enough N, the subsequence could hug the bottom of the lim sup to within epsilon (e). I don't know how to formalize this notion.
The last two steps of the proof are likely
-e < Snk - lim sup Sn < e
|Snk - lim sup Sn| < e