Given the sequences $\{a_n\}$ and $\{b_n\}$, if $\{a_n\}\leq \{b_n\}$ and $\{b_n\}$ converges, then $\{a_n\}$ is bounded.

I have to show that this affirmation is false, but I can't even see how this is false. If the greater sequence converges, shouldn't the lesser converge as well? And if it converges it is bounded... So how is it false?

(Sorry by my english btw, I'm not a native speaker)

  • $\begingroup$ Oh, I see... Thank you, drhab! $\endgroup$ – vairë Mar 20 '18 at 14:18

Take $b_n=0$ and $a_n=-n$ as counterexample.


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