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Aug
10
comment Matrix product notation
$\vec{\times}$? And why did you add the tag infinite-product?
Aug
10
comment How do I show that $ \sin x, \cos x$ really are in $ [-1,1]$ using series notion?
@MichaelHardy : If $x$ is real, then $\sin x$ and $\cos x$ are infinite sums of real numbers so they can only converge to a real number. And $(\cos x)^2+(\sin x)^2=1$ can either be derived as in the other answer by differentiation, or you can just compute the series as Cauchy products (which is basically brute force and I thought would be obvious to anyone familiar with series).
Aug
9
answered How do I show that $ \sin x, \cos x$ really are in $ [-1,1]$ using series notion?
Aug
4
comment Degree on Galois theory
And $\left[\Bbb Q(\sqrt[p]{2},\sqrt[q]{2}):\Bbb Q(\sqrt[p]{2})\right]=\cfrac{\left[\Bbb Q(\sqrt[p]{2},\sqrt[q]{2}):\Bbb Q\right]}{\left[\Bbb Q(\sqrt[p]{2}):\Bbb Q\right]}$
Aug
4
comment Degree on Galois theory
Well there's the case where $p=q$ and the case where $p$ and $q$ are coprime.
Jul
15
comment What is the relationship between the concept of a square root and a number's prime factorization?
If $n=2^{i_1}3^{i_2}5^{i_3}\dots$, then $\sqrt{n}=2^{i_1/2}3^{i_2/2}5^{i_3/2}\dots$ so for large numbers that are square, you can compute the factorisation of its squareroot and then double all exponents.
Jun
29
comment Satisfiable formula only over even structares
Hint: If your domain has an even cardinal, you can cut it in two parts (meaning that each element is in one of the parts and no element is in both parts) of equal size (meaning that you have a bijection between the two parts.
Jun
28
comment Need hint to solve a nasty integral.
Can't you just differentiate both sides?
Jun
24
comment Prove that set is bounded but has no max/min
$\frac{s+2}{2}$ is the middle of the segment $[s,2]$. You could take anything between $s$ and $2$ to find a contradiction but the middle is kind of the first thing you think of.
Jun
11
comment How to find the number of spanning trees for a cube?
You know that all spanning trees will have $8-1=7$ edges.
Jun
8
comment Question about polynomial ring and coefficients
Wouldn't $a=c=0$ work?
May
29
comment Existence of a minimizer for $\int_0^1|P(t)|\,{\rm d}t$.
You can restrict yourself to polynomials whose norm are $\le 1$ since you want to minimize the norm.
May
29
comment Existence of a minimizer for $\int_0^1|P(t)|\,{\rm d}t$.
@Farnight : Yes. $\alpha X + 1$ will work for any $\alpha$. The sup norm of this goes to $\infty$ as $\alpha$ goes to $\infty$ and since we're in finite dim, all norms are equivalent.
May
29
comment Existence of a minimizer for $\int_0^1|P(t)|\,{\rm d}t$.
@IvoTerek : Right >_<
May
26
answered Boundedness theorem question proof check
May
25
revised Euler's Equation
added 4 characters in body
May
24
comment Counting poles that are shared between $f$ and $g$
@pndev : There's still the problem of finding a "nice" $h$ so that your contour integral is actually defined. And then there's the fact that the bottom sum can be $0$ when the second summand is the opposite of the first, even if they are both not $0$.
May
24
comment Counting poles that are shared between $f$ and $g$
How about something like $$z\mapsto\cfrac{1}{\cfrac{1}{h(f(z))}+\cfrac{1}{h(g(z))}}$$ assuming you can find $h$ so that $|z|\to \infty \iff h(z) \to \infty$
May
24
comment Counting poles that are shared between $f$ and $g$
@Adayah : Whatever the OP meant by $D$. The interior of $\gamma$ I guess.
May
24
comment Counting poles that are shared between $f$ and $g$
@Adayah : I didn't notice the denominator was $0$. But yes, making a constant function was intended. Fixed trivial example : $$P(z)=\frac{\sum_{f_i=g_i\in D}1}{2\pi i}\frac{1}{z}$$