Rudy the Reindeer
Reputation
Next tag badge:
98/100 score
35/20 answers
Badges
8 51 142
Newest
Impact
~528k people reached

• 569 helpful flags
• 4,514 votes cast

# 2,963 Comments

 Nov 23 comment Orders of the elements in Z/8Z You're confusing additive and multiplicative notation I suspect. The neutral element here is $0$ not $1$. Nov 23 comment Cauchy Residue Theorem Application Craig, I left a comment in response to your comment to my answer in another thread. Since you probably won't be notified (as you seem to have deleted your comment) I am notifying you here. Nov 23 comment Examples of absolutely continuous functions that are not Lipschitz. @Craig You are right, it's not clear at all, I only hint at how to show uniform continuity. It would have been much better to use Lebesgue integrability of the square root function as in definition (2) here‌​. I will edit the answer when I have time. Thanks a lot for pointing out this shortcoming. Nov 21 comment Continuous function on a compact metric space is uniformly continuous @shilov You should look at the last line of the proof. The inequality should explain it. Nov 3 comment Fourier transform of the characteristic function @user929304 I see. I don't know if it makes sense, this is beyond my modest knowledge of Fourier transforms. It's not very useful but: Surely the decaying properties of $\mathcal F (\chi_{[c,d]}$ and $\mathcal F (\chi_{[0,1]}$ are almost identical? Nov 3 comment Fourier transform of the characteristic function @user929304 It's not clear to me what you mean. For example, "not differentiable in the usual sense" -- well apart from the points $c,d$ its derivative is 0, or am I missing something? And as for the FT of $\chi_{[c,d]}$: It looks to me like it's decaying. The expression is term one minus term two where each term is of the form one over something exponential times linear. But I might be missing something, it's been a while. Nov 3 comment invertibility in C*-algebra I don't understand why you would try to prove that $a-\lambda$ is invertible if by assumption ($\lambda \in \sigma (a)$) it isn't. What is your question? Nov 3 comment Is it true that $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$? Nov 2 comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$ @RobertoMilandro Yes, exactly. Nov 2 comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$ Regarding your second sentence: It's not possible for any ideal in $\mathbb Z$ to have more elements than $\mathbb Z$. Oct 29 comment Let $F\subseteq K$ and $V$ is a vector space over $K$ with a basis. What is the basis of $V$ over $F$? So... $K$ is a field with a basis $e_i$? Does that mean $K$ is also a vector space? Oct 3 comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$ @Tom-Tom Great, thank you. Oct 2 comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$ What's a primitive function? Oct 2 comment How to prove function $f(x,y)=\frac{1}{xy}$ is not uniformly continuous? Nicely done. ${}$ Sep 29 comment Branching points of the function $(z^2-1)^{2/3}$ Why are $\pm 1$ branch points? I looked up the definition and as far as I understand a critical point $z_0$ is called branch point it the winding number of a path around $f(z_0)$ is greater than one. In this case, $f(\pm 1) = 0$ but since there is no pole at $0$ it is not clear to me why the winding number around $0$ would not be $0$. What am I missing? Sep 28 comment Showing that an inclusion is null homotopic @morphic I don't remember. Sep 28 comment finding a linear transformation I might be missing something but is there any reason why you can't just define $\theta = \alpha \oplus \beta$? Sep 22 comment Reference for guided exercises in Group Theory Have a look at Joseph Gallian's Contemporary Abstract Algebra. It contains solutions to all odd numbered problems. Sep 19 comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$ @Potato Ok, right, of course it's enough to show they are constant on an open subset. I believe you but I don't yet see how to get the open subset. Concretely, if they are not constant each one has some open subset on which they are non zero, say $U_f, U_g$ and $U_h$. How do we guarantee that their intersection is non empty? Sep 19 comment $f,g,h$ be a holomorphic functions such that $|f(z)|+|g(z)|+|h(z)|=1$ So $g$ is the square root of $f$ but if $f$ is zero anywhere the square root is not differentiable in which case $g$ would not be holomorphic. So your answer assumes that $f,g,h$ are non-zero on $U$. Or am I missing something here?