Alan C
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 Dec 15 awarded Notable Question Dec 9 awarded Notable Question Jul 5 comment If $f(x)\ll1$ is it safe to assume that $f^{\prime}(x)\ll1$? What do you mean by $f(x) \ll 1$? Perhaps relevant is the function $f_\epsilon(x) = \epsilon \sin \frac{x}{\epsilon^2}$ as $\epsilon \to 0$. Mar 14 asked Example to show that multiplication by ideals and intersection of submodules do not commute Jan 8 awarded Notable Question Dec 8 awarded Caucus Dec 1 comment Why is the area of the circle $πr^2$? Actually, Archimedes used a method of exhaustion: en.wikipedia.org/wiki/Area_of_a_disk#Archimedes.27s_proof Nov 24 awarded Popular Question Sep 30 awarded Explainer Jul 20 accepted showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Jul 2 awarded Curious May 21 comment showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Let $\phi$ denote the monomorphism. Then exactness at $FA$ tells us $\ker Fg = \operatorname{im} \phi$. And then maybe it helps if we identify $\operatorname{im} \phi$ with $F(\ker f)$? (Maybe part of my confusion is due to the fact that I'm still used to thinking of kernels and images as objects?) May 21 comment showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Hmm, exactness at $F(\ker f)$ means that $F(\ker f) \to FA$ is a monomorphism. Our goal is to show that $\ker Fg = \operatorname{im} Ff$, so we need to extract some information about $\ker Fg$ from the monomorphism $F(\ker f) \to FA$, somehow? May 21 asked showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Jan 16 awarded Yearling Aug 14 awarded Popular Question Jun 26 comment How to show that this function (related to the zeta function) is even? Sorry, what do you mean by "harmonic sum"? A sum that arises when dealing with Fourier series? Jun 25 comment How to show that this function (related to the zeta function) is even? Wow, thanks! Could you explain how you were able to come up with all of that? Jun 13 asked How to show that this function (related to the zeta function) is even? May 21 asked Does $f, f' \in L^1([0, \infty))$ imply that $\lim_{x \to \infty} xf(x) = 0$?