You mean, because $d(\iota_X\Omega)$ is the divergence multiple of $\Omega$, then we can compare the coefficients of the terms in $2\,dx\wedge dy$ and in $\Omega$?
So $2\,dx\wedge dy$ has to be some functional multiple of $\Omega$. Can you easily deduce if that function is positive or negative? Well, at the north pole, it's obvious enough. Can the sign change in the hemisphere?
@Leaky: The world is not a happy place, altogether. My sympathies.
@TedShifrin I’ve been told that some people not in Hong Kong believe the government to have stepped back because of the misleading translation of Carrie Lam’s statement on June 15
The point is that $2\,dx\wedge dy$ is a nonzero multiple of $\Omega$ everywhere in the northern hemisphere (because the only place that form vanishes is where the tangent plane is perpendicular to the $xy$-plane).
What you said is intuitive but not a rigorous justification. It could vanish elsewhere.
Has anyone heard of a recent breakthrough by Giorgio Coraluppi in factoring large numbers. I got a flier in the mail that's worded vaguely but seems to aim at implying that he found some successful technique.
In high schools there's usually a set percentage for grades but not college
Professors just kinda decide what grades to give, some are more systematic than others
In my algebra class first two quarters, for instance, 67%+ was an A
(This was decided upon and told to us after the finals were graded)
Third quarter we didn't receive any info about grades. No grade cutoffs, no weighting (e.g. midterm is worth n%, etc). We just received some grades at the end
@Perturbative: With the traditional grading system, 80% is the lowest possible B (B–). But lots of departments/schools have different recommended grading schemes in core courses. As Demonark suggests, most college/university professors have lots of liberties in non-uniform courses.
The reason I ask is because I have to convert my grades from my universities grading system to the US standard (assuming such a standard exists) in the sign-up procedure for the GRE (just general at this point not subject test yet)
Nah @TedShifrin, Wikipedia tells me the British invented this system and we just picked it up. I mean we do get credited that we got a 95% on our academic record, but it falls into the same bracket as a 75% pass
Princeton Review is good for the content (though it doesn't cover integration on surfaces, and there's usually a question on that, and also their problems are a bit too easy since it's based on the older GRE)
@Perturbative otherwise it would be very unfair to you. You could be passing your courses, but to those people who receive your grades, it could look like you are failing.
@ÉricoMeloSilva lol re grades, in Madison I saw one class when I was looking for some earlier course materials which said that you got an A if it seemed like you'd pass the quals, B if you'd fail, F if you didn't work
A set with a unary operation is an algebra of type $(1)$ and a set with a trinary operation is an algebra of type $(3)$ in the language of universal algebra. Not sure if there's more specific terminology.
Let p be a prime ideal in a commutative unitary ring. Let x/1 be the usual embedding of R into the localization of R at p. Then if x/1 = 0 for all p \in SpecR we have x = 0
I am trying to prove this and was stuck with x \in Nil R in the end, any help?
What series should I compare it to? Would $\sum 1/n^2$ work? Also, how hard do you think it would be to calculate the sum of the original series, or at least an approximation?
@Cristopher Try to deduce the closed form for Fibonacci numbers and deduce that F_n / F_(n+1) converges to something bigger than 1, then use direct comparison test - comparing it to a geometric series
Let $B$ be a Banach algebra and let $B^\ast$ denote its corresponding dual space, normed with the supremum norm over the unit ball. It is (I think?) easy to verify that $\phi_n \to \phi$ in $B^\ast$ in norm if and only if $\phi_n \to \phi$ uniformly on the unit ball in $B$. A linear functional $\...
