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 Nov 11 comment Is there a proof of Bézout's theorem via residue theory? @TakumiMurayama Actually I think I'm being really stupid. Consider for example $f_1 = x, f_2 = y$. in $\mathbb P^2$. We have the right residue at $0$, and then I think we pick up the extra stuff when we switch charts and consider the line at infinity, so it all works out. The sum is zero, but one of the terms is exactly what we want, so we can just rearrange and get Bezout. Nov 11 awarded Nice Question Nov 11 comment Is there a proof of Bézout's theorem via residue theory? @TakumiMurayama So the global residue theorem is on p. 656, I think. But now I'm confused about something simple: the residue theorem says a certain sum is zero, but we want a sum that equals $\Pi d_i$. In particular, if we take the form to be $\frac{df_1}{f_1}\wedge\dots\wedge \frac{df_i}{f_i}$, doesn't the global residue theorem tells us the sum of the residues is $0$ and not the product of the degrees, as we desire? Nov 8 awarded Nice Answer Nov 6 awarded Necromancer Nov 4 awarded Notable Question Oct 29 awarded Popular Question Oct 25 awarded Yearling Oct 24 comment Other ways to compute this integral? @Unit You did the straightforward thing. I don't see anything wrong with that aesthetically. Oct 24 comment Unconventional mathematics books Mumford wrote approvingly of this book in his Notices article "Calculus Reform--For the Millions." Oct 24 comment Other ways to compute this integral? Perhaps use residues? This method already seems fairly painless... Oct 23 awarded Notable Question Oct 18 comment What is the purpose of showing some numbers exist? A minor correction: it's James Randi, not James Randy. (Though I admit your version is a little more funny...) Oct 14 comment Can we produce a long exact sequence in cohomology from more than just short exact sequences? @QiaochuYuan Thanks again! Could you perhaps say a bit more about how the period-3 behavior "falls naturally out the higher-categorical universal properties"? (Or was this implicit in what you had already written?) Oct 14 accepted Can we produce a long exact sequence in cohomology from more than just short exact sequences? Oct 14 comment Can we produce a long exact sequence in cohomology from more than just short exact sequences? Thanks! I was wondering, what references did you find helpful when trying to understand this material and get intuition for homological algebra? I find nLab almost impossible to read. Oct 14 asked Can we produce a long exact sequence in cohomology from more than just short exact sequences? Sep 30 awarded Popular Question Sep 25 awarded Popular Question Sep 24 comment Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD I don't think this quite works. You show that $2$ is not a unit times $\sqrt{10}$, but why couldn't it factor further, or factor as something else times $\sqrt{10}$? I think a better approach would be to prove that $2$ is irreducible using a norm argument, note that $2$ must also be a prime if the ring is a UFD, then show it does not divide $\sqrt{10}$.