what's the real value of $\sqrt2^{\sqrt2^{\large \sqrt2^{\sqrt2^{\unicode{x22F0}}}}}$?
Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?
Colorizing your terminal and shell environment? I spend most of my time working in Unix environments and using terminal emulators. I try to use color on the command line, because color makes the output more useful and intuitive.  What options exist to add color to my terminal environment? What tricks do you use? What pitfalls have you encountered?  Unfortunately, support for color varies depending on terminal type, OS, TERM setting, utility, buggy implementations, etc.  Here are some tips from my setup, after a lot of experimentation:   I tend to set TERM=xterm-color, which is supported on most hosts (but not all). I work on a number of different hosts, different OS versions, etc. I use everything from macOS X, Ubuntu Linux, RHEL/CentOS/Scientific Linux and FreeBSD. I'm trying to keep things simple and generic, if possible. I do a bunch of work using GNU screen, which adds another layer of fun. Many OSs set things like dircolors and by default, and I don't want to modify this on a hundred different hosts. So I try to stick with the defaults. Instead, I tweak my terminal's color configuration. Use color for some  (ls, grep, less, vim) and the . These commands seem to use the standard "". For example:  alias less='less --RAW-CONTROL-CHARS' export LS_OPTS='--color=auto' alias ls='ls ${LS_OPTS}'    I'll post my .bashrc and answer my own question Jeopardy Style. Kontact in Kubuntu 16.10 will not start because the Akonadi server will not start Sometimes when adding an object to the scene I see that all options (on toolbar or in window after pressing F6) are disabled. Can anyone tell me when can this happen? What is causing it and how to revert it - make it enabled again. It worked for me when I restarted Blender and reloaded the scene. However I would really like to know what can cause it? Access parent's parent from javascript object Failure to download extra data files - ttf-mscorefonts-installer This is an old problem that deserves a bugfix, but it's getting beyond a joke now and I can't seem to work around it.  I keep getting the dreaded failed To download extra data files error in relation to ttf-mscorefonts-installer:    Repeatedly asking it to try again doesn't help, additionally, repeatedly trying-  sudo rm -rf /var/lib/update-notifier/package-data-downloads/partial/* sudo apt-get --purge --reinstall install ttf-mscorefonts-installer   Isn't working either.  I just get at least one 404 error from one of the sourceforge links that stops it working-  Reading package lists... Done Building dependency tree        Reading state information... Done 0 to upgrade, 0 to newly install, 1 reinstalled, 0 to remove and 20 not to upgrade. Need to get 0 B/29.5 kB of archives. After this operation, 0 B of additional disk space will be used. Preconfiguring packages ... (Reading database ... 352049 files and directories currently installed.) Preparing to unpack .../ttf-mscorefonts-installer_3.4+nmu1ubuntu2_all.deb ... mscorefonts-eula license has already been accepted Unpacking ttf-mscorefonts-installer (3.4+nmu1ubuntu2) over (3.4+nmu1ubuntu2) ... Processing triggers for fontconfig (2.11.94-0ubuntu1.1) ... Processing triggers for update-notifier-common (3.168.2) ... ttf-mscorefonts-installer: processing... ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/andale32.exe Get:1 http://downloads.sourceforge.net/corefonts/andale32.exe [198 kB] Fetched 198 kB in 0s (339 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/andale32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arial32.exe Get:1 http://downloads.sourceforge.net/corefonts/arial32.exe [554 kB] Fetched 554 kB in 0s (575 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arial32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/arialb32.exe Get:1 http://downloads.sourceforge.net/corefonts/arialb32.exe [168 kB] Fetched 168 kB in 0s (306 kB/s)                                                 W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/arialb32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) ttf-mscorefonts-installer: downloading http://downloads.sourceforge.net/corefonts/comic32.exe Err:1 http://downloads.sourceforge.net/corefonts/comic32.exe   404  Not Found W: Can't drop privileges for downloading as file '/var/lib/update-notifier/package-data-downloads/partial/comic32.exe' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) E: Failed to fetch https://netix.dl.sourceforge.net/project/corefonts/the fonts/final/comic32.exe  404  Not Found  E: Download Failed Setting up ttf-mscorefonts-installer (3.4+nmu1ubuntu2) ...   The specific point at which it fails to download changed - it seems to be a sourceforge reliability problem, but this has now been going on weeks and results in annoying popups as above all the time.  How do we get this fixed and/or how can I work around it for now. Counting surjective functions We have $r$ objects and $n$ boxes. I have to count all the combinations possible if the objects and boxes could be both different. If that happens I can count the number of variations from $n$ to $r$ (number of functions between objects and boxes). I mean, $n^r$.  But if I have to count all the combinations possible if anyone of the boxes is empty ($r\ge n$). Now I have to count the surjective functions.  For example if I have $r$ objects and 1 box. The number of surjective functions is 1. Then, if I have $r$ objects and 2 boxes, the number of surjective functions is $2^r-2$. And finally if I have $r$ objects and 3 boxes, I will count $3^r-2\cdot[3\cdot2^r-3]$. How do I get the formula for $r$ objects and $n$ boxes? Indentation of continued lines in algorithmicx Trying to get the indentation right within the algorithmic environment I run into trouble, and all the solutions posted so far have not been able to solve my problem as I'd like to see it solved.  I want continued lines to have an indentation w.r.t the initial line (new to this forum and yet unable to post images).  However, the best I get with what I've found on this forum is either a fixed indentation for all continued lines (i.e., no difference if the initial line was indented or not), or the same indentation as the initial line (see MWE below).  Anybody has an answer to this?  \documentclass[10pt, A4]{report} \usepackage{algorithm} \usepackage{algpseudocode}  \begin{document}  \begin{algorithmic}\raggedright  \State Define N\_crf as the number of points on the circumference of the hyperstreamline, which will define its cross-sectional area at each r  \For {n = 1 : number of tracts}  \State \parbox[t]{\dimexpr\linewidth-\algorithmicindent\relax}{define N\_crf points creating a unit circle around r(n,i), in the plane perpendicular to t(n,i).}\strut  \EndFor  \end{algorithmic}  \end{document} Fibonacci Sequence and series limits 1) Let $F_1 = 1$, $F_2 = 1$, and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 3$.   How do you prove that  $$\sum_{n=2}^\infty \frac1{F_{n-1} F_{n+1}} = 1$$   $$\sum_{n=2}^\infty \frac{F_n}{F_{n-1} F_{n+1}} = 1$$   Do you even use the formula $n(n+1)/2$?   I tried using $F_{n-1} = F_n - F_{n-2}$ and $F_{n+1} = F_n + F_{n-1}$ and then trying to figure out how to substitute those, but I've been going around in circles. How would you solve this? What tips can you give me to solve this? Is there any website that teaches this? I tried searching google and youtube but none were helpful.   2) Let $s_x = \tan(2/x)$. Where does this become nonincreasing? While using monotonic limits to establish there is a limit.   I was guessing you need to use upperbound and lowerbound but doesn't it go to infinity? Moving Grub to a new drive to get rid of Windows Ill implement the some UI but its not working in the visualpage , can u know how implement jquery ui in viusalpage ,  Kindly tell the procedure ,     Im using this url its not working ,,,,, Recently upgraded to Ubuntu 18.10, having two problems.  Easiest to explain: when I open "settings", go to "privacy", select "screen lock", I get the popup window with the screen lock settings, but everything is grayed out:   Second issue: If I step away from the machine for long enough (seems to be 5 minutes), the screen blanks. Hitting a key or moving the mouse wakes it up. But when it wakes up, the only things on the screen are the icon bar at the left and the top bar with status icons on the right end. The rest of the screen is blue, not my normal lock screen image. The screen isn't locked, it doesn't prompt for a password, it's just...blue.  I can move the mouse pointer around the screen, the icons react if I click on one, I can bring up the popup with volume/brightness controls on the top bar. But if the pointer is on the blue background, neither left nor right button clicks do anything.  Now, if I press ctrl-alt-F1 from there, I get a lock screen where I can enter my password. Then I get the blue screen back, but if I press ctrl-alt-F2 I get my normal screen (with running applications) back.  ctrl-alt-F2 without going through the lock screen first does nothing.  I'm not finding anything while searching that matches either of these sets of symptoms. Suggestions? Trying to understand what happens with a brokerage firm's customers when it goes bankrupt (case of study: Lehman Brothers) I'm trying to understand how secure it is to own mutual funds/ETFs, not in terms of market volatility etc., but in terms of judicial security (i.e. what happens to your holdings if the firm goes bankrupt). To understand it, I have read this article about the bankruptcy of Lehman Brothers:  Note: From now on, I'm always referring to investors who own funds/ETFs managed by Lehman Brothers, not by investors who invested in Lehman Brothers or subprime mortgages (e.g. S&amp;P 500 ETF investors). From the above article, what I have understood is that the funds/ETFs managed by Lehman Bros. were shifted to other brokerage firms to be managed by them. Is this what actually happened? Still, what happens with the investors if, hypothetically, no brokerage firm in the world wants to manage these financial products? How to use grep on column? I want to apply grep on particular column in column command.  myfile.txt  3,ST,ST01,3,3,856 3,ST,ST02,4,9,0234 6,N1,N101,2,3,ST 6,N1,N102,1,60,Comcast 6,N1,N103,1,2,92   My Command:  column -s, -t &lt; myfile.txt | grep -w "ST"   Here I want to only grep the pattern ST in 2nd column. How to do this ?  Expected Result:  3       ST            ST01              3            3            856 3       ST            ST02              4            9            0234 When is "self" required? I have been using classes for only a short while and when I write a method, I make all variables reference self, e.g. self.foo.  However, I'm looking through the wxPython in Action book and notice that "self" isn't used all the time. For example:   import wx  class TextFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Text Entry Example',             size=(300, 100))         panel = wx.Panel(self, -1)         basicLabel = wx.StaticText(panel, -1, "Basic Control:")         basicText = wx.TextCtrl(panel, -1, "I've entered some text!",             size=(175, -1))         basicText.SetInsertionPoint(0)         pwdLabel = wx.StaticText(panel, -1, "Password:")         pwdText = wx.TextCtrl(panel, -1, "password", size=(175, -1),             style=wx.TE_PASSWORD)         sizer = wx.FlexGridSizer(cols=2, hgap=6, vgap=6)         sizer.AddMany([basicLabel, basicText, pwdLabel, pwdText])         panel.SetSizer(sizer)   The one below does use "self".  import wx class ButtonFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Button Example',             size=(300, 100))         panel = wx.Panel(self, -1)         self.button = wx.Button(panel, -1, "Hello", pos=(50, 20))         self.Bind(wx.EVT_BUTTON, self.OnClick, self.button)         self.button.SetDefault()     def OnClick(self, event):         self.button.SetLabel("Clicked")   If I remember correctly, "self" is reference to a particular instance of the class, so when is it not necessary? Is there a general rule of thumb? Does leaning (banking) help cause turning on a bicycle? I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the bike's momentum keeps it moving in the direction you were going, and since your wheels have friction against the ground, the top of the bike moves forward relative to the bottom of the wheels. The top of the bike going north while the bottom of the wheels go northwest will understandably cause you to topple. So to counteract this and keep you from falling over, leaning into the turn is necessary. But is there also a direct causal relationship -- that leaning will cause the bike to start to turn? If I start leaning left, I will turn left... but maybe that's because I know that if I don't turn the steering wheel left, the bike will fall over (to the left). I experimented with unruly turns of the steering wheel when I was a kid, and got my scrapes and bruises. Now that I'm a cautious and sedate adult I'm not anxious to experiment that way. :-) (I also want to ask why airplanes bank into a turn... they don't have the same issues as a bike, i.e. the bottom part has no special friction against the ground. But that would probably make the question too broad.) Is there any way to save the order of spaces in Mission Control? How long does it take for a black hole to form for an external observer? The well-known fable of an astronaut sending signals out to an external observer while falling toward an event horizon states that the time lapse between such signals becomes greater even if in the astronaut sends them out periodically (as judged in his inertial frame). When viewed from earth and weighing time-dilation due to the gravitational field of the collapsing star, how is it possible that a black hole can form in finite time (for any external observer) if it takes an infinite amount of time to "see" events occurring at the event horizon? I've just got my first follower, and I'm wondering if I can get a second person to follow me. Is the game limited to one or two follower(s) or does it allow for a large number of followers? It really seems handy to me to have some followers protect me when I draw attention from a larger group, or when I try to steal something where I really shouldn't... Async call generates " Error: Can't wait without a "fiber", even with _wrapAsync QGIS locked into fullscreen mode on Ubuntu 12.04