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 Yearling
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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 : $$P(z)=\frac{\sum_{f_i=g_i\in D}1}{2\pi i}\frac{1}{z}$$
May
7
comment Derivatives and integrals of polynomials of two variables
The partial derivative doesn't give you that much about $p$. If $r(x,y) = p(x,y) + q(y)$, then $\partial r / \partial x = \partial p / \partial x$. Probably not what you're searching for but $R[X,Y] \equiv R[X][Y]$ as rings and $R[X] \equiv R[X] \times R$ as vector spaces via $p \mapsto (p', p(a))$ (where $a$ is a constant). If you combine those two facts, you get $R[X,Y]\equiv R[X,Y]\times R[X]$ as vector spaces via $p\mapsto (\partial p / \partial y, (x\mapsto p(x,a))$.
May
2
awarded  Yearling
Apr
29
comment Zeroes of sin(x)
Might help: math.stackexchange.com/questions/349143/…
Apr
25
comment When can I divide both sides of an equation if one side is zero
For equality, you can multiply both sides by the same number (and therefore also divide by any non-zero number since that's just multiplication by the inverse of the number). Whether the number is positive or negative doesn't matter. It does however when you have an inequality because if you multiply by a negative number, you have the inverse the inequality.
Apr
17
comment Power set equinumerosity. Is this proof correct?
$H(B)$ isn't defined. $B\in \mathcal P(B)$ which is the codomain of $H$. And to prove that a function is the inverse of another, you just prove that when you compose them (on both sides), you get the identity.
Apr
17
comment Power set equinumerosity. Is this proof correct?
You didn't define $H$, you only gave its domain and codomain. $H:X\mapsto \{f(a) / a \in X\}$. And I think it'd be easier to build its inverse and prove that it is indeed its inverse instead of proving that it's bijective.