Rudy the Reindeer
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 Sep 11 comment What tools would I use to answer the following topology question? Thank you. And which part in the linked document is relevant to the question? It seems to me that the document only deals with finite dimensional products but humour me and point me to the relevant theorem in the document. Sep 11 comment What tools would I use to answer the following topology question? So: compact implies sequentially compact implies every sequence has a convergent subsequence. Sep 11 comment What tools would I use to answer the following topology question? Can you state the Bolzano Weierstrass property? Sep 11 comment What tools would I use to answer the following topology question? What is N? The natural numbers or a natural number? Sep 10 comment Arbitrary Intersection of Bounded Sets Is Bounded @Josué Exactly. I was just about to post an answer but now that you figured it out yourself I will not. Sep 10 comment Proving with completeness axiom @MarianoSuárez-Alvarez I assumed he meant if $a \in E$ then $a \le 0$. Sep 1 comment Analysis in $R^n$ @user262860 Yes, it is false. Aug 29 comment Analysis in $R^n$ Personally, I feel that the linear-algebra tag would be more suitable to your question. Aug 29 comment Characterization of the weak topology Where you wrote $M$ in your definitions should that be $A$? Aug 28 comment Finding the order of permutations in $S_8$ This is a very nice answer. I allowed myself to correct a few typos, hope you don't mind. Aug 20 comment $\arctan (x) + \arctan(1/x) = \frac{\pi}{2}$ What happens if $x<0$? Aug 20 comment $\arctan (x) + \arctan(1/x) = \frac{\pi}{2}$ What happens if $x < 0$? Aug 19 comment If $f$ is one to one show that $f(a) \in \partial \Omega$ @zhw. THe argument I had in mind when I first read this post was that since $f$ is injective, if $f(a)$ was in $f(G-a)$ then $f(a) = f(b)$ for some $b$ in $G-a$ thereby contradicting injectivity of $f$. Aug 19 comment If $f$ is one to one show that $f(a) \in \partial \Omega$ @tattwamasiamrutam It's not helpful to denote elements in $\Omega$ by $g$. Aug 19 comment If $f$ is one to one show that $f(a) \in \partial \Omega$ @zhw. I am pinging on behalf of OP. Aug 19 comment Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$ Thank you for your reply. Is there a reason why you wrote $n \alpha$ instead? I find it confusing, especially because you also write $n/(2\pi)$ where I think it should also be the fractional part thereof. But I might be missing something. Aug 19 comment Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$ Nice answer but I don't understand why you write you guessed wrong: I don't understand why we cannot represent a complex number $a + bi$ as the matrix in your answer. It seems to me that we can interchange $b$ and $-b$ as we like. What am I missing? Aug 19 comment Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$ @SalechAlhasov Your link leads merely to a login page. Maybe you can post a new link? Aug 19 comment Analytic functions on $\mathbb{H}$ such that $f(i)=3i$ Interesting question! Aug 19 comment If $f$ is one to one show that $f(a) \in \partial \Omega$ It looks ok to me. Where you write ...,so there exists a $\delta > 0$... etc. I would have written $F$ or $\widetilde{f}$ or something like this because it's an analytic extension of $f$ and not $f$ itself (as it is defined at $a$ and $f$ isn't).