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1h
comment Complex Numbers: Im$(\frac{12}{z-7})=1$
It is still wrong: you want to multiply by the complex conjugate, which is $\overline{z}-7$, not $\overline{z}+7$.
1h
comment Complex Numbers: Im$(\frac{12}{z-7})=1$
This suggestion is false: multiplying $z-7$ by $z+7$ gives $z^2-49$, which is almost never real. The correct factor to multiply top and bottom by is $\overline{z}-7$, if you want to write down explicit formulas.
20h
comment $p$-completion of a $\mathbb{Z}_p$-module
It's simpler than that: a f.g. $\mathbf Z_p$-module looks like $\mathbf Z_p^d \oplus A$ for some finite abelian $p$-group $A$, and this is complete in its $p$-adic topology.
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comment What resources are there for learning Russian math terminology?
I've wondered for a while where the "elsewhere on this site" is that Alex wrote his remarks about motivation, and finally I stumbled onto it, so I just want to record it here for posterity in case anyone else is curious about that in the future: meta.math.stackexchange.com/questions/1617/…
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comment Who named “Quotient groups”?
@MartinBrandenburg: In what way is Quotientengruppe more precise that Faktorgruppe? Do they not mean exactly the same thing? If you use the terminology Faktorring and Faktorraum as well, then as Serge Lang would say the terminology is functorial with respect to the ideas. As a contrast, the similar-sounding label "quotient field" is completely unlike quotient group, quotient ring, or quotient space, which might be why the name "fraction field" is used too. (While "factor group" and "factor ring" in English sound archaic but not too weird, "factor space" in English sounds very bizarre.)
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comment Do these definitions make sense?
@blue: It presumably means "is it also true" about these other constructions. I fixed the English.
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revised Do these definitions make sense?
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revised References for mathematical theory of summability of divergent series
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comment Who named “Quotient groups”?
@MartinBrandenburg: There is a link to Holder's paper in Dubuque's answer. Click on it and look at the start of section 5 (page 32) where Holder discusses equivalence classes (he introduces the term quotient on the previous page). I think the answer to your question is that he identified things, in the sense of viewing $G/H$ as a set of equivalence classes rather than a set of coset representatives, but your German is far better than mine so read the paper directly. By the way, in German today are Faktorgruppe and Quotientengruppe used equally often, or is one more common than the other?
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comment Does anyone have a good reference on calculating contour integrals around the unit circle (numerically or otherwise)?
I agree such usage would be problematic; I was just checking if you knew it. Is the polynomial itself nasty (you say 6 of the 12 roots are "known", and are the ones outside the unit circle "known" too)?