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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).
Aug
19
comment Slick proof that if an open set contains $\mathbb Q$ it has all irrational numbers, except a countable amount.
@dREaM Oh I see, the "not countable" referred to the missing numbers.
Aug
19
comment Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$
Nice answer. Where you write $n\alpha$ is in that interval didn't you mean $\operatorname{fractional part}(n\alpha)$ is in that interval?
Aug
19
comment Slick proof that if an open set contains $\mathbb Q$ it has all irrational numbers, except a countable amount.
@dREaM What is wrong with taking $\mathbb R$ minus $\{i_1, \dots, i_n\}$ where $i_k$ are irrationals?
Aug
18
comment Basis for a linear space
@DavidP Tru dat. I will not delete my comment though as I think it might be useful to others who read this thread.
Aug
18
comment Basis for a linear space
Showing that the set spans the space is not enough: one has to show that it's linearly independent, too.
Aug
9
comment Are all matrices linear operators?
But I would like to be convinced otherwise, of course.
Aug
9
comment Are all matrices linear operators?
In particular, if $A$ is such a matrix and $x$ some vector and we let $Ax$ be the usual multiplication then this seems to me is not a map $\{1,\dots,m\}\times\{1,\dots,n\} \to \mathbb{K}$ but a map $\mathbb R^m \to \mathbb R^n$.