In a set theoretic context you've got this von Neumann/Godel set theory, you start with the idea of a class, and a set is a type of class that can be contained in another class. So some types of classes are sets, others are not, they're called proper classes
@Daminark Here's an interesting point to make. If $f : X \to \Bbb C$ is meromorphic with say a pole $p \in X$, locally near a deleted neighborhood of $p$, it looks like $1/z^k : \Bbb C \to \Bbb C$. So you can extend $f$ to an actual holomorphic map $\tilde{f} : X \to \Bbb P^1$ by sending $\tilde{f}(p) = \infty$
So meromorphic functions always extend to holomorphic maps to $\Bbb P^1$
Let R be the rectangle joining the midpoints of the sides of quadrilateral Q having vertices (±x,0) and (0,±1). Calculate: limx->0^+ = (PerimeterofR)/Perimeter of Q
Not actually construction, maintenance I think. A sewer broke and they've torn up a street trying to fix it. They must've cut an underground wire related to the internet at some point
@Balarka so as $z\to\infty$, $f(z)\to \frac{a}{c}$, so I think the way we extend to a holomorphic function on $\mathbb{P}^1$ is to let $f(\infty) = \frac{a}{c}$ (if $c=0$, call that $\infty$)
@Daminark But yeah, you're claiming as $f' \neq 0$ (because the determinant is nonzero, as our matrix was in $\text{GL}(2, \mathbf{C})$), $f$ is locally a biholomorphism everywhere (by inverse function theorem). Why is it globally a biholomorphism?
@Dodsy @Abcd @LeakyNun I choose to leave the site and you people send me a bunch of email notifications excusing me of having duplicate accounts? If you have an issue contact a moderator. I'm not your babysitter and it's not me job to mediate when you people decide to get in an argument. I've asked you to leave me alone, and that wasn't a joke. Stop trying to contact me. Thank you.
for that accusation I should flag him. that was a bit offensive him accusing that guy so insistently. I'm too lazy and don't really care. I just want people to quit bugging me.
@Semiclassical since I'm not going to be back on, please give @Dodsy a figurative slap in the back of the head for me would ya? He's acting all paranoid about me again claiming other users are me. Kind of annoying to everyone. Even if he thought it was a username change it was still kind of dumb of him to act like that.
@Daminark Yeah I'm not entirely sure why we aren't allowed $\det A = \pm 1$ in this context either. If I were to restrict that I'd assume $\omega_1/\omega_2$ and $\omega_1'/\omega_2'$ are both in the upper half-plane.
sure there are flag spammers, but they could be brand new users that don't even use chat. Heck, it would be MO users playing a mean prank for instance.
@nitsua60 see the above comments and the linked reply I originally made. I don't wish to report it using a flag as it's probably not flag worthy. However, I would appreciate it if you could find the time to make some kind of post warning people about random accusations. Dodsy was being quite rude with ABCD.
