@TedShifrin "Let $F$ be any curve, $P = (0, 0)$. Write $F = F_m +F_{m+1}+···+F_n$, where $F_i$ is a form in $k[X,Y ]$ of degree $i$, $Fm \neq 0$. We define $m$ to be the multiplicity of $F$ at $P = (0, 0)$, write $m = m_P (F)$. " Which is this $m$ in this case??
I just want to say thanks for closing my art post the other day. I reposted it on Facebook where it belongs according to you guys. You're all wrong though and are unaware. Good luck. I'll be back when I've put some good hours in at work and have time to study the unbroken symmetries that are in Math lala land.
You're all tripping pretty badly and are also unaware of that.
What trick am I missing? This problem is too nasty to solve the normal way
"Let $\textbf{n}$ be the outer unit normal of the elliptical half-shell $S: 4x^2 + 9y^2 + 36 z^2 = 36, z \geq 0$, and let $\textbf{F} = 5 y \textbf{i} + 5 x^2 \textbf{j} + 5 (x^2 + y^4)^{3/2} \sin e^{\sqrt{xyz}}\textbf{k}$. Find the value of $\mathop{\iint}_S \big(\nabla \times F) \cdot \textbf{n}~\textrm{d}\sigma$
Hint: One parametrization of the ellipse at the base of the shell is $x = 3 \cos t, y = 2 \sin t, 0 \leq t \leq 2 \pi$. But you can avoid a line integral altogether."
It was originally closed as not being math within the scope of the help center, if I recall. I'm not him, so I won't comment on the amount of effort involved.
@TedShifrin did you want me to go all the way back to the left here, or was my right simplification the right direction?$$\sum \limits_{n=1}^\infty \frac{1}{n(n+1)(n+1)!}=\sum \limits_{n=1}^\infty \frac{(n-1)!}{(n+1)!^2}$$
if this is wrong i wont bother you with it anymore because i clearly need to read more about these things $$e\sum \limits_{n=1}^\infty \frac{1}{n(n+1)^2}$$
my brothers when they were in uni spent every saturday working all day as a rule(and they worked in the week by going to all lectures and tutorials), and sunday was rest day
i am starting to live and breathe math, and my parents said they will ban me from doing more than two hours of math a day, unless i do all my other classes for atleast as long lol
So was this wrong? i will go and do calculus if it is wrong $$\sum \limits_{n=1}^\infty \frac{1}{n(n+1)(n+1)!}=e\sum \limits_{n=1}^\infty \frac{1}{n(n+1)^2}$$
balarka gave me hammocks book of proofs(set theory) to do first
also, if $J=(a_1, \dots, a_n)$ is a regular sequence in a Noetherian local ring $A$, why is $J^k/J^{k+1}$ isomorphic as an $A$-mod to a sum of copies of $A/J$?
@robjohn i was trying to say that since $\sum \limits_{n=0}^\infty \frac{1}{n!}=e$ then, $\sum \limits_{n=0}^\infty \frac{1}{an!}=e\sum \limits_{n=0}^\infty \frac{1}{a}$
@robjohn so it is because $\sum \limits_{n=0}^\infty \frac{1}{n!}\sum \limits_{n=0}^\infty \frac{1}{n!}\ne \sum \limits_{n=0}^\infty \frac{1}{(n!)^2}$?
ok ok i probably dont get it, so i will have to go read some stuff. so sums are treated with parentheses, i just cant multiply the inside of the sum, only note that the sum of two series is the series of their sum, but not multiplication
if you're seeing it, @Kaj, then you have two circles and in the projective sense if you delete a point in one of the circle and replace it by the point at infinity, then it precisely looks like the plot of an elliptic curve, no?
how do i write the the set $\{2,4,8,16,32,64,\dots \}$ in set builder notation? i see that it is $x=2^k$ do i write $\{x\in\Bbb{Z}:x=2^k, k\in\Bbb{Z}\}$?
OK, @Kaj. Now so the ellcurve y^2 = x^3 + ax + b over C is just a torus, which is Z \times Z. So the m-torsion points (i.e., the points (x, y) in the ellcurve such that (x, y) + (x, y) + ... + (x, y) is (0, 0) after m times summing, where plus is the elliptic curve group operation) form the group Z/m \times Z/m
