Alan C
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 Sep8 asked How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$? Aug24 awarded Organizer Aug24 revised Domain, Co-Domain & Range of a Function added terminology tag Aug24 suggested approved edit on Domain, Co-Domain & Range of a Function Aug9 awarded Teacher Aug9 awarded Commentator Aug9 comment How do I prove the divergence of this series? @Didier: Oh yeah, thanks for pointing that out! Aug9 comment How do I prove the divergence of this series? @Asaf: Hmm, that's a good point. If the original problem was with $\frac{1}{\log log n}$, I guess my solution was overkill. Aug9 answered How do I prove the divergence of this series? Jun8 comment How does the parallelogram law imply the existence of an inner product for a given norm? Thanks! I'm sorry I didn't find that when I searched for this question. Jun7 asked How does the parallelogram law imply the existence of an inner product for a given norm? May27 comment Understanding the Schwarz reflection principle Thanks! That was the statement and construction given by the book, and while I could understand it, I didn't understand why my construction didn't work. May27 awarded Scholar May27 comment Understanding the Schwarz reflection principle Thank you! This was exactly my problem! I had assumed that $f(\overline{z})$ was holomorphic because it was a pretty "nice and simple" function. I just started studying complex analysis, so I had the definition of holomorphic memorized without much intution, but I understand the idea a lot better now! May27 accepted Understanding the Schwarz reflection principle May27 asked Understanding the Schwarz reflection principle Jan31 awarded Supporter Jan16 comment Defining the determinant of linear transformations as multilinear alternating form Aha thanks! I wonder how I overlooked the linearity of $T$. Hm... but I'm also wondering if this could be done in a way similar to the Steinitz exchange lemma. Suppose we order the $e_i$'s and $f_i$'s so that for all $0 \leq k \leq n$, $f_1, \ldots, f_k, e_{k+1}, \ldots, e_n$ span $V$. Then we could go from $vol(Te_1, \ldots, Te_n)/vol(e_1, \ldots, e_n)$ to $vol(Tf_1, \ldots, Tf_n)/vol(f_1, \ldots, f_n)$, replacing one vector at a time. (And the reason the ratio stays the same is because $T$ is linearity.) Jan16 awarded Student Jan16 comment Defining the determinant of linear transformations as multilinear alternating form Adding one row to another does not change the volume, while multiplying a row by a scalar changes the volume by that scalar factor. So if we go from $e_i$'s to another basis, say $f_i's$, then the ratio $vol(f_1, \ldots, f_n)/vol(e_1, \ldots, e_n)$ is the product of all the scalar multiplications. But I don't see why this is the same as $vol(Tf_1, \ldots, Tf_n)/vol(Te_1, \ldots, Te_n)$