There is no bijective holomorphic map between $\mathbb{D}-\{0\}$ and $\{z|0<r<|z|<R\}$.
Non-existence of a bijective analytic function between annulus and punctured disk
There is an experimental timeline view for questions now available on meta ONLY! (Now working on SO, SF, and SU as well)  This is partially motivated by comments about how difficult it is to follow very active questions which have a lot of activity, and also the feedback on the API which was heavily dominated by "we need to know what happened in this time range" type responses.  It can only be accessed through URL hackery at the moment. To get to it, enter question URLs like so:  https://meta.stackexchange.com/posts/{id}/timeline  This is a chronological timeline of everything that happened on a question, including   initial question ask answers  revisions comments closure, deletion, reopen, undelete, etc votes   all based on when they happened in chronological order.  We are thinking about making this a fourth tab on the question, like so:  Timeline | Oldest | Newest | Votes  Please try it out and provide feedback. It is still a little rough, so we are not looking for highly detailed bug reports, just more general feedback.  Timeline view for this question: Quoting within $(command substitution) in Bash My computer wont shutdown If I try to shutdown my computer it simply takes me back to the login-screen. I looked around and found :  Type in terminal:   sudo gedit /etc/default/grub Find the line: GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" Change this to:GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi=force" Save the file and close the file.  Finally, in terminal: sudo update-grub   But now there is a new problem when I try step 5 it says:  *myname*@ubuntu:~$ sudo update-grub [sudo] password for *myname*:  /usr/sbin/grub-probe: error: cannot find a device for / (is /dev mounted?). *myname*@ubuntu:~$    I am new whit linux and dont know what to do. Using a comma before "but" How to fix pagination for custom loops? Show that $X^2$ and $X^3$ are irreducible but not prime in $K[X^2,X^3]$.   My reasoning is as follows:  Since the only ways $X^2$ and $X^3$ can be factored in $K[X^2,X^3]$ are $X^2 = X^2 * 1$ and $X^3=X^3*1$ it follows that $X^2$ and $X^3$ are irreducible.  To show that they are not prime in $K[X^2,X^3]$ I argue that $X^2\mid X^3*X^3$ but $X^2\nmid X^3$ and $X^3\mid X^4*X^2$ but $X^3\nmid X^4$ or $X^3\nmid X^2$.  Is that correct? Sum and product of Martingale processes Given two Martingale processes $(X_t)$ and $(Y_t)$, are their sum $(X_t+Y_t)$ and their product $(X_t \times Y_t)$ also Martingale?  If not, will the two $(X_t)$ and $(Y_t)$ being independent grant their sum and product Martingale? Thanks! How to peel hard boiled eggs easily? This is one of the most annoying duties in the kitchen, for me.  What are yours tips and tricks to peel hard boiled eggs easily? How to minimize the ink-to-data ratio for pgfplots Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$ Why does my DIY "solar panel circuit" show battery voltage and not solar panel voltage? Time Traveler steps on a butterfly, changes everything I heard of this in high school, but never learned its title or author- supposedly the aforementioned worm butterfly would have played a part in evolution that caused the extinction of the dinosaurs (instead of that meteor most people blame now). This story might even have been parodied on a certain Simpsons Halloween Special (the one where Homer accidentally makes a time machine trying to fix the toaster). Faster language/keyboard swapping I like making a habit to use the different languages I study, to keep that knowledge fresh. So I like typing in those languages when I get the chance. But swapping keyboards under OSX is just a little too cumbersome.  For example, I was just typing the name of one of my co-workers in its original 汉子 form instead of as an English transliteration. It's nice. It reminds me to pronounce her name properly, with tone, etc., which otherwise doesn't come naturally. The transliteration of her name is especially misleading. Everyone at the company is pronouncing it wrong.   But to swap into writing 汉子 I have to mouse up to the top menu bar, select a new keyboard, type, mouse back up to the top bar, and then select back into English. I know there's a keyboard shortcut, but with 5 different keyboards active in my menu, cycling through 5 to get to the one I want feels just as cumbersome.  Is there a way to attach a hotkey to a specific keyboard, or some other way to make swapping character sets lighter? Do I need to apply for a visa to enter South Korea as a tourist on an Australian passport? Do I need to apply for a visa to enter South Korea as a tourist for a few days when travelling on an Australian passport? Or will I be able to get one on arrival? Setting or modifying a (system wide) environment variable in cmd.exe I am looking for a convenient way to add and/or modify and/or delete an environment variable from the command line. Particularly, I find myself at times in situations when I have to add a few variables in cmd.exe.  I'd be grateful if someone showed me a non-GUI way to modify (that is: to add a new directory to) the %PATH% variable.  The change should be be permanent, not just for duration of the cmd session. Understanding my electrical panel I just purchased .  I'll be installing it in my RV.  Current will be supplied by a 12VDC to 120VAC, 3000W inverter.  I'll be using Single-Pole Type BR breakers.  Here's a picture of the box:    My current understanding is that I must install a grounding bar to the box.  This is my current understanding of how to connect the breaker to the main supply.:    Here is my understanding of how I would wire in new circuits:    Does this look right?  I would really appreciate your help -- I've been beating myself over the head about this. I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $ Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$ Receiving Push Notifications while in background My overall upgrade went well, but I am left with a critically lingering issue of mysql-server not being able to install itself, and nothing I am trying gets it to work.  This is the error I see when trying to install/reinstall it:  Setting up mysql-server-5.7 (5.7.11-0ubuntu6) ... Job for mysql.service failed because the control process exited with error code. See "systemctl status mysql.service" and "journalctl -xe" for details. invoke-rc.d: initscript mysql, action "start" failed. dpkg: error processing package mysql-server-5.7 (--configure):  subprocess installed post-installation script returned error exit status 1 dpkg: dependency problems prevent configuration of mysql-server:  mysql-server depends on mysql-server-5.7; however:   Package mysql-server-5.7 is not configured yet.  dpkg: error processing package mysql-server (--configure):  dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                    Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Errors were encountered while processing:  mysql-server-5.7  mysql-server E: Sub-process /usr/bin/dpkg returned an error code (1)   I've tried completely removing it, though doing so attempts to install MariaDB because of dependencies (?). Any suggestions on what I can do to fix this would be most welcome.  EDIT: Looks like I'm not the only one: