- #1
Mr Davis 97
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Homework Statement
Let ##\{a_n\}## be a bounded sequence such that every convergent subsequence has limit ##L##. Prove that ##\lim_{n\to\infty}a_n = L##.
Homework Equations
The Attempt at a Solution
I'm not really understanding this problem. Isn't ##\{a_n\}## a subsequence of itself? So isn't it immediately the case that ##\lim_{n\to\infty}a_n = L## by the hypothesis?
EDIT: Nevermind. I notice now that it says every convergent subsequence.