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5h
comment Non-Empty Finite Subset $U$ of $\mathbb{R}$ is not Open
Yes, that's fine. It would be enough to state that specifically $x-\frac12\delta\notin U$ with $x=\min U$.
5h
comment What are the facts used in each step of this proof?
I'd even suppose $=$ instead of $\le$ in that place
6h
comment for which values of $\theta$ does this equation $x^{\cos\theta} +y^{\sin\theta }=1$ have solutions in integers .?
If $\cos\theta> 0$ and $\sin\theta\ge 0$ then $x=0$, $y=1$ is a solution. If $\cos \theta= 0$ and $\sin\theta=1$, then $x=1$, $y=0$ is a solution. There is clearly no solution with exponents $-1$ and $0$. Remains the case of noninteger exponents, at least one negative.
7h
comment Natural action of $S_n$ on $\{ 1,2,\dots,n \}$
@sandstone it is equivalent because the existence of $g$ with $gx=y$ is equivalent to $x,y$ being in the same orbit.
1d
comment Does it make sense to apply the Manhattan metric to an arbitrary graph?
Wouldn't the Manhatten metric simply mean that the distance between two vertices is the minimal number of edges for a path between them?
1d
comment $\mathbb E[X_i\mid X_1,…,X_n]=\mathbb E[X_i]$
This reminds me a bit of the fun task to expand the polynomial $(x-a)(x-b)(x-c)\cdots (x-z)$ :)
1d
comment tetrahedron problem with center and reflections
right tetrahedron = the three angles at one of the vertices are right angles? This does not seem to match the image
2d
comment Question on one point compactification
Yes, "the" embedding here is the inclusion map
2d
comment what is the counter example to minimality of coloring a graph in BFS manner?
Your algorithm is not specific. Which colour from the set colorsUsedSofar but NotUsedByItsAdjacents?
2d
comment A Chain of Subsets of $\mathbb{R}$ Without any Good Countable Subchain
What does "code" mean here? View the binary digits of $x\in\mathbb R$ as a relation $\subseteq\omega\times\omega$ ?
2d
comment A Chain of Subsets of $\mathbb{R}$ Without any Good Countable Subchain
@GregoryGrant An explici injection of $\mathbb R^2$ into $\mathbb R$ is easy and should then suffice as well.
2d
comment A Chain of Subsets of $\mathbb{R}$ Without any Good Countable Subchain
@GregoryGrant Yes, $\mathbb R\cong \mathbb R^2$. - But I donÄt see how that helps.
2d
comment Prove this is a rectangle
@DavidK Sorry, mixed up $A$ and $C$, corrected now. We have $CD'=AB$ from the rectangle $ABCD'$ and $AB=CD$ is given
2d
comment Prove this is a rectangle
@soktinpk Alright, then I show that the assumption $D\ne D'$ is absurd. That's not fishy
2d
comment Why doesn't the derivative of a holomorphic function vanish in a border maximum?
Let $G=\mathbb C$, $f(z)=1-z^2$, $K=[0,1]$, $a=0$. Then $\max_{z\in K}|f(z)|=1=|f(a)|$. And we have $f'(a)=0$.
2d
comment Show every chain has an upperbound?
Your example, the set of all numbers $<\sqrt 2$ does not have a maximal element, so it is certainly not automatically true that you have a max element.
2d
comment $A$ is diagonalizable if $A^8+A^2=I$
OR: A muiltiple root of $f(X)=X^8+X^2-1$ is a common root of $f$ and $f'$, but $f'(X)=8X^7+2X$ and $Xf'(X)-8f(X)=2X^2+8$, so a multiple root $\lambda$ would have $\lambda^2=-4$, $\lambda^8=256$, so $f(\lambda)=256-4+1\ne0$, i.e., there is no multiple root.
2d
comment Most efficient algorithm to distribute n n-bit strings among n people
Is it on purpose that $N$ the number of people equals $N$ the length of bitstrign, but not necessarily $n$ the number of ones?
2d
comment circle-shaped wave
Wouldn't $y=\sin x$ look nicer anyway?
2d
comment Mathematical concepts named after mathematicians that have become acceptable to spell in lowercase form (e.g. abelian)?
So nobody mentioned eigenvalues (after the German mathematician Karl-Friedrich Eigen) and binomial (after the Italian Giuseppe Binomi)? ;) -- Seriously, I have often heard the question from whose names these adjectives are derived :)