How to differentiate $\lim\limits_{n\to\infty}\underbrace{x^{x^{x^{...}}}}_{n\text{ times}}$?
Derivative of $x^{x^{\cdot^{\cdot}}}$?
I need to somehow retrieve the client's IP address using JavaScript; no server side code, not even SSI.  However, I'm not against using a free 3rd party script/service. I am trying to install Ubuntu 12.10 for quite some time, and passing hurdles one by one. Now I am in a situation as follows.  I have got a PC and 10 GB HDD which will be totally dedicated to Ubuntu so no option of Wubi and dual boot.  I was trying to install from DVD, but it is getting stuck at "Out of frequency" error. So I had to adapt for USB boot option. But my PC is USB non bootable, so workaround is "Plop Boot Manager". So I am doing the installation procedure as follows:   starting  from a CD drive which is having plop installed. opting for for USB boot in plop options. booting begins from USB. monitor eventually gives "out of frequency" error press Shift+Alt+F1 to get the terminal. open the grub with sudo nano /etc/default/grub. do necessary changes. sudo update-grub.   Now here I am getting error as follows:   /usr/sbin/grub-probe:error:failed to get canonical path of /cow.     My system is   P4 3.06 GHz, 1 GB ram , 10 GB HDD without an OS, monitor CRT lg StudioWorks (7 years old). Mobo Mercury P4 266a NDMx (865 equivalent). The whole system is perfectly in working condition under XP, but it is USB non bootable, and all other devices working perfectly.  What should I do next? general solution sum of two uniform random variables aY+bX=Z? is there a general solution to that? I have seen simple examples for Y+X=Z but I was wondering how this would be with rescaling? What is `$?` ? Is it a variable? The question is pretty straight forward. I can get the exit code of the previous command by using $?. But what exactly is it?  I don't think it is a variable, because you can't have any special characters in the name of variable other than _.  foo?foo=10   will result in the error: foo?foo=10: command not found  So if it is not a variable, what is it? Are there others like it? I am seeking suggestions on what may be going in with an iMac I am currently troubleshooting, as it’s displaying behaviour I do not recall seeing before.  Short story  This iMac refuses to boot up. It gets the Apple logo, gets past the progress bar, and then gets stuck on the grey screen for about two minutes before rebooting itself. However, what makes this odd is that I can:   Start the iMac in Target Disk Mode and use it to successfully boot up other Macs. In doing so everything seems to work perfectly fine. Successfully boot the iMac from an external drive and everything seems to work perfectly fine.   Long story  I was presented this iMac about 2 weeks ago as it refused to bootup. That is, it would commence booting up and cycle through the Apple logo and progress bar, but after the progress bar completed it would remain on the grey screen for a couple of minutes before rebooting itself and doing the same thing all over again.   To address this I undertook the following troubleshooting steps:   Resetting SMC - failed Resetting NVRAM - failed Starting up in Safe Mode - failed Starting up in OS X Recovery Mode – failed Starting up in OS X Recovery Mode via the internet – failed Undertook an extensive hardware test using Apple Hardware Test (AHT 3A213) - passed Started iMac in Target Disk Mode and retested hard drive using Scannerz on another iMac - passed Started iMac in Target Disk Mode and reformatted the hard drive and did a clean install of Mac OS X El Capitan 10.11.6 - successful Migrated data from a Time Machine backup - successful   After these steps I tested the iMac for four days with no issues in terms of booting up and using the computer. On the fifth day I needed to manually import seven Apple Mail mailboxes. I did these one by one and six of them imported within minutes.  The last mailbox was showing as being 270 GB in size. I knew this was inaccurate, but I decided to import the mailbox so I could do a mailbox rebuild to correct whatever corruption had taken place. This import took over 12hrs to do but seemed to work fine and Mail was displaying the emails.  I then tested the iMac on and off for another day to ensure it had no problems booting up. This was successful.  I then decided to initiate the mailbox rebuild, but as soon as I did the screen went black and stayed that way regardless of any keyboard shortcuts I tried using. I waited an hour, forced a reboot, and ever since the iMac has returned to its original behaviour of not booting up – it would get past the progress bar and stay on the grey screen for a while before rebooting itself and starting the whole vicious cycle again.  I have again retested the hard drive, processor, RAM and Video Ram by starting the iMac from an external hard drive and using a combination of the following packages:   Apple Hardware Test (AHT 3A213) Scannerz TechTool Pro Memtester (under the Homebrew subsystem)   And now I have a situation where I can boot the iMac from external hard drives, and also use it in target disk mode to boot up other Macs, but cannot use it to boot from its own internal drive.  At present I have isolated the internal hard drive and am running a scan to check for any malware.   In the meantime, I am wondering:   Has anyone come across a similar scenario and, if so, what was the cause? Assuming I find no malware, do I go through the reformat/clean install/migration process again, but this time not import the last mailbox and see whether the iMac works fine? Any other suggestions?   iMac specs are as follows:   iMac (27”, mid 2011) 3.1 GHz Intel Core i5 8 GB RAM AMD Radeon HD 6970M 1024 MB 1 TB 3.5” SATA HD Mac OS X El Capitan 10.11.6 Where to start learning Linear Algebra? I'm starting a very long quest to learn about math, so that I can program games. I'm mostly a corporate developer, and it's somewhat boring and non exciting. When I began my career, I chose it because I wanted to create games.  I'm told that Linear Algebra is the best place to start. Where should I go? Is there a way to programmatically determine if a font file has a specific Unicode Glyph? I'm working on a project that generates PDFs that can contain fairly complex math and science formulas.  The text is rendered in Times New Roman, which has pretty good Unicode coverage, but not complete. We have a system in place to swap in a more Unicode complete font for code points that don't have a glyph in TNR (like most of the "stranger" math symbols,) but I can't seem to find a way to query the *.ttf file to see if a given glyph is present.  So far, I've just hard-coded a lookup table of which code points are present, but I'd much prefer an automatic solution.  I'm using VB.Net in a web system under ASP.net, but solutions in any programming language/environment would be appreciated.  Edit: The win32 solution looks excellent, but the specific case I'm trying to solve is in an ASP.Net web system.  Is there a way to do this without including the windows API DLLs into my web site? Add a binary to my path I have an executable. I want to execute the executable in terminal with name only like other commands.  I can put my executable in /usr/local/bin or I could add its PATH to ~/.bashrc. Both will work.  What is better?  Is there  any difference? New top bar doesn't show hot threads across Stack Exchange sites Tony's Private life in Spider-Man: Homecoming I really don't know how to do this in terms of spoilers, but here goes...  After watching the end of Homecoming, it appears that       Tony and Pepper are very much back together.   Is there any in-universe explanation for this change from the way the universe seemed to be in Civil War? Could I have a hint for testing the convergence of the following series please?  $$\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$$  Edit  The integral test does not work because $\int_1^n\frac{1}{(\ln x)^{\ln x}}dx$ has not an elementary primitive.  Thank You. How to download all files from Ubuntu One? Permutation count of AABBC Given a string:  $AABBC=A^2B^2C^1$   I am trying to find the Total Permutations (this may be incorrect):  $\dfrac{5!}{2!\cdot2!}=30$  My question is how would I find the partial sums (perhaps the wrong choice in words) when added together would give an index such that:   $AABBC=1$ $ABABC=2$ $CBABA=29$ $CBBAA=30$   (30 might be the wrong number here but is suppose to be the last)   I have tried to draw out a tree structure to get an idea and thought with as the minimum:  $CAABB$  $4(\dfrac{4!}{2!\cdot2!})$ + 1  And:  $CABAB$  I would get something like:  $4(\dfrac{4!}{2!\cdot2!}) + 0 + 1(\dfrac{2!}{2!}) + 0 + 0$  But I am missing something here. How would I find the sums needed for $BACAB$ ?  More specifically I am trying to find the index of a word that is arbitrarily long in alphanumeric.  So the string may also be something like:  $AAAAABBBBDDEEFFFGGGGGHIIIIJJJJKLMOOOPZZZZZ$ How do exchanges match limit orders? Why isn't sizeof for a struct equal to the sum of sizeof of each member? Why does the sizeof operator return a size larger for a structure than the total sizes of the structure's members? I know what a set is. I have no idea what a class is.   As best as I can make out, every set is also a class, but a class can be "larger" than any set (a so-called "proper class").  This obviously makes no sense whatsoever, since sets are of unlimited size. It's not like you get up to 25 elements and go "oh, hey, sets are limited to a maximum of 20 elements, so we'll have to call this 25-element thing something else".  Does anybody know what the actual difference between a set and a class is?  Several people have pointed out that you can write paradoxes which involve sets. I get that. But where do classes come into the picture? setSystemUiVisibility(SYSTEM_UI_FLAG_LAYOUT_HIDE_NAVIGATION) does not work Why is empty set an open set? I thought about it for a long time, but I can't come up some good ideas. I think that empty set has no elements,how to use the definition of an open set to prove the proposition. The definition of an open set: a set S in n-dimensional space is called open if all its points are interior points. Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia) "She will be visiting" vs. "she will visit" When she goes to Mexico, she will be visiting Chichen Itza. When she goes to Mexico, she will visit Chichen Itza.  Is there a particular difference in meaning, or it is just the matter of style?