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Nov
29
comment How is half-contour integration possible?
@AlexR. I am. Apologies. I meant a contour that does not stop at any finite point (that is, goes off to infinity in both directions).
Nov
19
comment Is there a general way to prove series and products are modular?
@user45195 The mild moral qualm about reposting this question is stronger than my attachment to reputation.
Oct
26
comment Extension field of finite degree
Do you mean finite?
Oct
25
comment condition for homeomorphism
Are $A,B$ open sets?
Oct
24
comment Path connected iff the action of $\pi_1(Y,y)$ on $p^{-1}(y)$ is transitive.
If I have been unclear, please ask for clarification or rephrasing of my answer.
Oct
24
comment Prove that the number of automorphisms in $\mathbb Q[\alpha]$ equals $1$ $(|Aut\mathbb Q[\alpha]|)=1$
@Walterr if $\alpha, \beta, \gamma$ are the roots, then $f(a_1 \alpha+a_2 \alpha^2 +b_1 \beta +b_2 \beta^2 +c_1 \gamma +c_2 \gamma^2+d)=a_1 f(\alpha)+a_2 f(\alpha)^2+b_1 f(\beta)+b_2 f(\beta)^2 +c_1 f(\gamma)+c_2 f(\gamma)^2+d.$ Thus $f(l)$ for any $l \in L$ is determined by the action of $f$ on the three roots.
Oct
24
comment Prove that the number of automorphisms in $\mathbb Q[\alpha]$ equals $1$ $(|Aut\mathbb Q[\alpha]|)=1$
@Walterr I mean that one of $f(\alpha)=\alpha, f(\alpha)=\omega \alpha, f(\alpha)=\omega^2 \alpha$ will occur, and for each of these options you have $2$ choices as to what $f(\alpha \omega)$ is (which, along with $f(\alpha)$, determines $f(\omega^2 \alpha)$).
Oct
23
comment How to visualise Bollobas' 1965 theorem?
I have crossposted to MO.
Oct
21
comment So why isn't $\Bbb R^n = \oplus _{n = 1}^{m}\Bbb R^n$
Decomposed uniquely.
Oct
20
comment $|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
I will accept an answer when I've read into this a little more.
Oct
18
comment $|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
How would you apply Zorn here? The obvious partial ordering by inclusion doesn't work directly.
Oct
18
comment $|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
@AsafKaragila I searched for a while and found similar questions that seemed similar but simply cited the result.
Sep
8
comment Best Sets of Lecture Notes and Articles
@AlexYoucis The Katok link has stopped working.
Jul
28
comment how to show that $\mathbb{Q}[\sqrt[3]{2}]$ is a field? (by elementary means)
See here for a proof that if $a$ is algebraic, $F(a)=F[a]$.
Jul
23
comment How is $ \sum_{n=1}^{\infty}\left(\psi(\alpha n)-\log(\alpha n)+\frac{1}{2\alpha n}\right)$ when $\alpha$ is great?
You seem to have forgotten the $\pi^2$ term in the final line.
Jun
28
comment Binomial Congruence
See if you can adapt this proof.
Jun
23
comment Does the index of a curve determine the asymptotic behaviour of certain vector fields?
@DavidH I think I'm talking about the index of the curve, sorry for the confusion of terminology (regardless, I'm talking about the thing Needham is talking about in Visual Complex Analysis, page $\approx 498$).
Jun
23
comment Does the index of a curve determine the asymptotic behaviour of certain vector fields?
@DavidH $$\frac{1}{2\pi} \int_{\gamma} \frac{v(p)_x}{|v(p)|^2}dy- \frac{v(p)_y}{|v(p)|^2}dx.$$
Jun
22
comment Does the index of a curve determine the asymptotic behaviour of certain vector fields?
I think Needham calls it the winding number, I'd be happy to know the proper name for this.
Jun
22
comment Does the index of a curve determine the asymptotic behaviour of certain vector fields?
@DavidH Let $v(p)$ be the vector associated with the point $p$. I define winding number to be the number of anticlockwise revolutions $\frac{v(p)}{|v(p)|}$ makes as $p$ moves along $\gamma$ in a closed loop. What you're referring to seems to be the case when $v(p)=p$.