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Jun
24
comment Solution to differential equation $f^{(n)}-(n+1)f^{(n-1)}-(n+1)nf^{(n-2)}-\dotsc-(n+1)!f=g$
For $n=5$, the characteristic polynomial in $r^5 - 6r^4 - 30r^3 - 120r^2 - 360r - 720$, and PARI-GP confirms that its Galois group is $S_5$, so it is not solvabel by radicals
Jun
23
comment How can I prove that $f$ doesn't have all real roots $\forall a\in\mathbb{C}$
Clear-cut and convincing, unlike the other incomplete answers so far
Jun
23
revised How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
added 1608 characters in body
Jun
23
revised How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
added 1608 characters in body
Jun
23
comment How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
"please describe the case of faces of dimension 1 and 2 in an introductory way with lots of details. " ? That's not the kind of request I satisfy because I don't do other people's homework for them, I only help.
Jun
23
revised How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
added 9 characters in body
Jun
23
revised How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
added 580 characters in body
Jun
23
answered How do I show that $B$ has an infinite number of extreme points, but no faces (sides) of dimension $1$ or $2$?
Jun
23
accepted Infinite matrix is injective if all its upper left minors are invertible?
Jun
23
asked Infinite matrix is injective if all its upper left minors are invertible?
Jun
22
comment A constructive method for finding a subfield $\mathbb{K}$ such that $Gal\left(\mathbb{C}\left(x\right)/\mathbb{K}\right)$ is isomorphic to $S_3$.
@JyrkiLahtonen But the decomposition field of $y^3+Ay+B-(x^3+Ax+B)$ over (${\mathbb C}(x^3+Ax+B)$) does work, doesn't it
Jun
22
comment A constructive method for finding a subfield $\mathbb{K}$ such that $Gal\left(\mathbb{C}\left(x\right)/\mathbb{K}\right)$ is isomorphic to $S_3$.
@Lubin you are right. In fact, to get a normal extension ith group $S_n$ one must first take an irreducible polynomial of degree $n$, then take the normal closure. So here I should have started with a polynomial of degree $3$ not $6$
Jun
21
comment How to combine the four Theorems in order to prove the statement?
Is your main question (how to combine the four theorems to get the statement) in Feller's book also ? At which page ?
Jun
20
comment A constructive method for finding a subfield $\mathbb{K}$ such that $Gal\left(\mathbb{C}\left(x\right)/\mathbb{K}\right)$ is isomorphic to $S_3$.
Off the top of my head : I think most ${\mathbb C}(f(x))$, where $f$ is irreducible of degree $6$, will do. The minimal polynomial of $x$ over $\mathbb K$ will then be $f(x)-c$ with $c\in{\mathbb K}$. Do you know about Luroth's theorem ? en.wikipedia.org/wiki/L%C3%BCroth%27s_theorem
Jun
19
accepted Which ZFC axiom schemes are reducible to a single axiom?
Jun
19
asked Which ZFC axiom schemes are reducible to a single axiom?
Jun
15
comment Two sets $X,Y \subset [0,1]$ such that $X+Y=[0,2]$
It is indeed, not true at all for the Cantor set you have constructed. In fact, one can show for a large family of Cantor sets, there is a dichotomy between the sets that are "too large" (not nice) or "too small" (not satisfying $X+Y=[0,1]$). I'll write more about this if I have the time
Jun
15
comment Is this polynomial irreducible over the rationals?
If the put $A_p(x)=\sqrt{\frac{T_p(x)-1}{x-1}}$, then $A_p(\cos(\theta))=\frac{\sin(\frac{p\theta}{2})}{\sin(\frac{\theta}{2})}$ (because of the identity $\cos(t)-1=-2\sin^2(\frac{t}{2})$). So $A_p$ is "almost" a Chebyshev polynomial of the second kind.
Jun
14
accepted variant of Heine-Borel theorem : countable subcovering of segment covering in $\mathbb R$
Jun
14
comment variant of Heine-Borel theorem : countable subcovering of segment covering in $\mathbb R$
Ok, so you really meant "writing this relatively open set as A countable union"