Alan C
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 Mar14 asked Example to show that multiplication by ideals and intersection of submodules do not commute Jan8 awarded Notable Question Dec8 awarded Caucus Dec1 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 Nov24 awarded Popular Question Sep30 awarded Explainer Jul20 accepted showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Jul2 awarded Curious May21 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?) May21 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? May21 asked showing exact functors preserve exact sequences (abelian categories, additive functors, and kernels) Jan16 awarded Yearling Aug14 awarded Popular Question Jun26 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? Jun25 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? Jun13 asked How to show that this function (related to the zeta function) is even? May21 asked Does $f, f' \in L^1([0, \infty))$ imply that $\lim_{x \to \infty} xf(x) = 0$? May6 awarded Caucus Apr14 accepted Transpose of a linear operator on functions Apr11 comment Transpose of a linear operator on functions Ah, thanks! I was thinking of using the divergence theorem, but I wasn't sure if it was applicable (partly because I didn't know what was the exact space of functions $L$ was acting on).