how to define $x^\sqrt 2$?
Can you raise a number to an irrational exponent?
How many individual lights can an arduino control I want to use a regular Arduino board to control LEDs - what is the most lights I can control individually from the board?  Is there a tutorial on how to hook it up? Oddly wide spaces in subsection title I have a problem, this is what it looks like:     And this is the code:  \subsection{Bakterienst\"amme und Anzuchtbedingungen}   Where does the huge whitespace come from? Imported 3D scan displays texture in editor, but renders without texture I am new to blender and I have a 3D scan of a stone tablet (which I am unfortunately not able to share, so I will try to be as detailed as possible) which was imported as OBJ and MTL files.  The editor displays the texture and mesh perfectly, but when I render the scene (pressing F12) the texture is not there.  I am trying to use blender to reduce the file size of the tablet for use in a three.js visualizer for a website.  I have tried exporting the file as a JSON file (as well as several other file formats to the same effect) for use in my three.js webapp and thought it was an issue with three.js, but after seeing that blender did not render the tablet with the texture I now believe it is an issue with my blender configuration. I am unable to find within blender or online any way to check what current resources I have displayed and what options I have with them.  I have not applied a mesh or texture to the object, but when I do so it renders with the generated texture applied in the default pink.  I am confused as to where the disconnect is between the editor and the renderer. I am still figuring out what is important and where to find all the relevant information, so any help on that regard would be very much appreciated.  Here is what blender looks like for me with the sensitive parts censored (can't be too careful these days):   I have looked at this question:  And there is no material overwriting the texture - I have not assigned a material to the tablet at all. EDIT: In regards to the duplicate answer, I looked at that one as well and the issue I have is that it doesn't have an actual texture file that I can just put on it.  The OBJ MTL files come with their own file that can't be applied directly to the model.  Blender read the OBJ MTL files and recreated the object inside blender algorithmically - and now I need to know how to get blender to tell me where that texture is and how I can get it to show up in the render.  The texture is not on my hard drive, but entirely within blender which is the issue I am having. Salesforce query on profile not working on user language change I have a query on profile like  profilename = [Select name from profile where id=:userinfo.getUserprofileid ].name  Now I have a check in  VF page  like  profilename  == 'System Administrator' . this works fine if the logged in user language is english. If the user language is different then profile name will be  'System admin' in that language . So how to prevent this beahviour?   Also  is there any particular field in profile which I can use  to identify the profile is system admin? so that I can have check on that field instead of checking for name which is causing the problem, for example I think modifyall filed is only checked for system admin. Is selenium webdriver capable of database testing? After reading so many answers and forums it makes me confused. Some people say: Selenium webdriver is a browser automation tool and it has nothing to do with the database. And some other showing JARs and code that how we can connect selenium to the database and we can test database using selenium webdriver. So I would really like to know if we can do database testing using selenium? If yes then which databases tool it supports like Mysql, SQL server, Oracle... And if selenium is not suitable for database testing then please recommend to me the best tool for database testing. how do I prove that $1 > 0$ in an ordered field? I've started studying calculus.  As part of studies I've encountered a question. How does one prove that $1 &gt; 0$?  I tried proving it by contradiction by saying that $1 &lt; 0$, but I can't seem to contradict this hypothesis.  Any help will be welcomed. Given fields $M/E/F$, why does $[M:F] = [M:E][E:F]$? Let $M$ be a finite extension of $E$ and let $E$ be a finite extension of $F$. Then $M$ is a finite extension of $F$ and $[M:F] = [M:E][E:F]$.   Is there an easy explanation and/or proof for this theorem? My instructor gave an incomplete proof in class but got stuck and I'm kind of confused of what's going on. How to graphical remote control an Ubuntu server? I've tried googling and .  I'm connecting my Windows 7 SP1 machine to an Amazon EC2 Ubuntu cloud server, Ubuntu 10.04 LTS. What I have done is   Enabling Remote Desktop in Ubuntu (, ) Connect to my server using 1)  and 2)  &ndash; I don't use  since it contains viruses.   But all of those result in Connection failed. I'm giving up!  More Detail Ubuntu server to remote to: Ubuntu 10.04 LTS (codename lucid)  My Windows: Windows 7 SP1 Use laptop trackpad as graphics tablet I know and have observed that the the division algorithm can be used to convert any number in the decimal system to the binary system. However, I have tried searching for an intuition of why this method works, and I just can't seem to see anything, although I know what type of intuition I am trying to make out.   So, my question is why we can use the division algorithm to convert between the decimal bases and any other number bases?   An example from the decimal system to binary would be appreciated. What is an "index out of range" exception, and how do I fix it? Failed to allocate memory: 8 Viewer-independent copyable spaces at the beginning of a line? I need to include a couple of Python code listings, where the indentation of the lines (using some number of spaces) is significant. I would like for the code listings to be copyable, so the spaces at the beginning of the line need to be be copied along with the text.  This question has been asked in various ways before (e.g. , or ). Those questions focus on making line numbers uncopyable, though.  Making the spaces at the beginning of a line copyable seems to be harder: "I am not sure it is possible to specify in the PDF (at least in a viewer-independent way) that the indentation should be copied too" (). At , Philippe Goutet suggests a solution (turning the spaces into visible spaces, and coloring them in the background color so that they appear invisible) that works using Acrobat Reader, but not all readers. He says "It works under Acrobat Reader and it's extremely pleasant to be able to quickly copy/paste code without problem (perhaps the problem can be circumvented by writing direct PDF code to tell that it's a space, I've never had the time to try)".  Is it possible to produce a PDF with a code listing with copyable real spaces at the beginning of a line?  Minimal example: The line return x should start with four spaces.  \documentclass{article}  \begin{document} \begin{verbatim} def myfunction(x):     return x \end{verbatim} \end{document}   I know that I could attach the code to the PDF as a file, but that's not what I want. Someone who gives unsolicited explanations in a condescending way Integrating Floor Functions $\int_0^{1102} \lfloor{x^{1/2}}\rfloor \mathrm{d}x$ I want to find a general formula to calculate the integral of such function (x&gt;0) Could someone kindly help me? $$\int_0^{1102} \lfloor{x^{1/2}}\rfloor \mathrm{d}x$$ Thank you! Nvidia driver updated - mixed versions of 304.88 and 319.32 My problem is that after trying to update my driver through the additional drivers GUI I can't boot Ubuntu with GUI anymore, since Xorg says the kernel module is of version 304.88 (The old version before I updated) but the driver components are of version 319.32 (The new version)  This is the output of dpkg -l | grep nvidia  dkpg -l | grep nvidia ii nvidia-304 : 304.88-0ubuntu0.0.3  NVIDIA binary Xord driver, kernel module and VDPAU library ii nvidia-319 : 319.32-0ubuntu0.0.1  NVIDIA binary Xord driver, kernel module and VDPAU library ii nvidia-common : 1:0.2.44.2  Find obselete NVIDIA drivers ii nvidia-current : 304.88-0ubuntu0.0.3  Transitional package for nvidia-current ii nvidia-settings : 304.88-0ubuntu.0.0.3  Transitional package for nvidia-settings ii nvidia-settings-304 : 304.88-0ubuntu.0.0.3  Tool for configuring the NVIDIA graphics driver ii nvidia-settings-319 : 319.32-0ubuntu.0.0.1  Tool for configuring the NVIDIA graphics driver   That's the output of that file.  The message startx gives me is:  NVIDIA: API mismatch: the NVIDIA kernel module has version 304.88, but this NVIDIA driver component has version 319.32. Please make sure that the kernel module and all NVIDIA driver components have the same version.     Fatal server error:    no screens found   I understand that something went wrong during the update, so I wonder how to fix this so that the remaining parts of 304 are removed and replaced with 319. I don't know hwere to start because I thought that nvidia-current was the one that would update to 319 and so reinstalling that didn't work. And I googled and found that somebody said to try to install/reinstall/uninstall this package: nvidia-current-updates-dev  But I didn't have that package installed so it did not help. Other than that, I am clueless. I hope the information I provided will be enough so I can get an answer soon.  EDIT:  lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 12.04.3 LTS Release: 12.04 Codename: precise  uname -a Linux SQuad 3.2.0-52-generic #78-Ubuntu SMP Fri Jul 26 16:21:44 UTC 2013 x86_64 x86_64 x86_64 GNU/LINUX I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model.  For example, in the validation dataset, I have the true value for the dependent variable, retention (1 = retained; 0 = not retained), as well as a predicted retention status for each observation generated by my regression analysis using a model that was built using the training set (this will range from 0 to 1).  My initial thoughts were to identify the "correct" number of model classifications and simply divide the number of "correct" observations by the number of total observations to calculate the c-statistic. By "correct", if the true retention status of an observation = 1 and the predicted retention status is > 0.5 then that is a "correct" classification. Additionally, if the true retention status of an observation = 0 and the predicted retention status is &lt; 0.5 then that is also a "correct" classification. I assume a "tie" would occur when the predicted value = 0.5, but that phenomenon does not occur in my validation dataset. On the other hand, "incorrect" classifications would be if the true retention status of an observation = 1 and the predicted retention status is &lt; 0.5 or if the true retention status for an outcome = 0 and the predicted retention status is > 0.5. I am aware of TP, FP, FN, TN, but not aware of how to calculate the c-statistic given this information. Hiding downvoted questions silences important discussions on Meta I just noticed a particular MSE post today on a topic I care about that was posted almost a week ago, which I entirely missed before. I'm a pretty avid MSE user, and this happens quite rarely to me.     was created by an SE employee, and is essentially the final answer to , which is the 10th most upvoted MSE post with a bit more than 900 upvotes right now. So it's kind of an important post, and on a topic I care about, but I still missed it entirely until it was linked in a comment somewhere else.  The reason I missed it is because it's heavily downvoted. This means that as it has below -8 score, it's hidden from the home page entirely, drastically reducing the visibility of the post. In particular, the negative score removes all visibility a question usually receives from being bumped due to edits, new answers and bounties.   Many of the recent heavily-downvoted Meta posts by SE have been featured manually, which grants them a lot of visibility beyond the particular meta site. This masked the problem pretty efficiently, but it is more of a workaround, and one that isn't applicable to all situations.  Voting means something different on meta sites, and not every downvoted question should be hidden from view. Closed downvoted questions can certainly still be affected by the usual rules on the home page, and that should cover the vast majority of questions that actually have a purpose being on the home page. But open questions should be displayed on the home page on meta sites even if they're heavily downvoted. bash if -a vs -e option Both about -a and -e options in  is said:  -a file     True if file exists. -e file     True if file exists.    Trying to get what the difference is I ran the following script:  resin_dir=/Test/Resin_wheleph/Results  if [ -e ${resin_dir} ] ; then     echo "-e "; fi  if [ ! -e ${resin_dir} ] ; then     echo "! -e"; fi  if [ -a ${resin_dir} ] ; then     echo "-a"; fi  if [ ! -a ${resin_dir} ] ; then     echo "! -a"; fi   /Test/Resin_wheleph/Results exists and is a directory. And this is what I get:  -e -a ! -a   which seems to be a little strange (notice -a and  ! -a). But when I use double brackets (e. g. if [[ -e ${resin_dir} ]]) in the similar script it gives reasonable output:  -e -a   So:    What is a difference between -a and -e options? Why -a produces a strange result when used inside single brackets? Changing my Apple ID's email: address is not available