Let (an) be a bounded (not necessarily convergent) sequence, and assume
lim bn = 0. Show that lim(an*bn) = 0. Why are we not allowed to use the Algebraic Limit Theorem to prove this.
Last edited by ajj86; Oct 22nd 2008 at 05:59 PM.
Reason: Title Error
Let (an) be a bounded (not necessarily convergent) sequence, and assume
lim bn = 0. Show that lim(an*bn) = 0. Why are we not allowed to use the Algebraic Limit Theorem to prove this.
I appreciate your answer to my question. I've been having a lot of trouble understanding real analysis. This class reminds me a lot of abstract algebra. I guess proofs just aren't my forte.