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I have a previous similar question. I'm working out that one with the answerer, but I'm trying to gain insight from a different angle, especially in approaching these problems.

I must establish that two vectors $A$ and $B$ are equal asymptotically (length of vectors, $n\to\infty$). I consider the error vector, $e=A-B$ and try to show that $e\to 0$ as $n\to\infty$.

I then show that for each element $e_i$ of the error vector, $\Vert e_i\Vert_2\to 0 $ as $n\to\infty$. How can I proceed from here? Is this sufficient to say that the two vectors are equal in some sense?

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Not sure I quite follow, but suppose $A$ is all zeros except for a one in its last component, and $B$ is all zeros except for a one in its next-to-last component. Then each component of the difference goes to zero but the difference doesn't go to zero as the number of components goes to infinity.

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    @ArturoMagidin I see. Thanks for clarifying. I guess I will need to show that $\Vert e \Vert\to 0$ and not component wise.2011-12-27