Proving isometries of the plane are bijective
Prove that every isometry on $\mathbb{R}^2$ is bijective
Have Google index different languages at the same URL instead of just the default (English) I have a multilingual PHP site. I have set English as the default language.  The language changes automatically according to the browser settings. If it is French, the site will be seen in French.  However in the Google search results, even if I have the browser in French, the English language appears in the results. How can I fix that?  To be clear I don't want to use subdomains or URLs like www.example.com/fr/. I would like it to work like Facebook. After using `networksetup -setdnsservers Wi-Fi "8.8.8.8" "8.8.4.4"` how do I clear them? I'm looking to script a temporary DNS server change to override the DHCP response I get from the network. I've figured out I can use networksetup but once we're done testing. Before I push to production, I figure I should know how to undo this.  How can I script to clear these changes and restore the settings the network provides now as if I never ran the following script?  networksetup -setdnsservers Wi-Fi "8.8.8.8" "8.8.4.4"   It's not feasible to save any the previous settings and I'm looking to remove the setting so that the actual new values can be retrieved from the network as opposed to saving what the settings were previously so I don't save an old value that is no longer correct.  Basically, I'm looking to ipconfig /renew on macOS. About two weeks ago I had a problem with my PC that my brother wrote a question about at .  I still haven't solved the problem, so my PC is unusable now.  Now I think that it would be simpler to re-install both Win7 &amp; Ubuntu than repair them, but there're some data on their partitions. I want to recover this data.  These partitions are not mountable for some reason. I don't know why.  sudo fdisk -l about the problematic partitions:     Device    Boot      Start         End      Blocks   Id  System /dev/sda1            2048     147912703    73955328   83 Linux /dev/sdb2            206848   174079999    86936576    7  HPFS/NTFS/exFAT   And in GParted:      And the error of the mount command:  Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   And the exact same message for /dev/sda1  How can I recover my data from those HDDs?  EDIT     I have tried to specify the type of the drive:  $ sudo mount -t ext4 /dev/sda1 /olddisk mount: wrong fs type, bad option, bad superblock on /dev/sda1,        missing codepage or helper program, or other error        In some cases useful info is found in syslog - try        dmesg | tail  or so $ sudo mount -t ntfs /dev/sdb2 /olddisk NTFS signature is missing. Failed to mount '/dev/sdb2': Invalid argument The device '/dev/sdb2' doesn't seem to have a valid NTFS. Maybe the wrong device is used? Or the whole disk instead of a partition (e.g. /dev/sda, not /dev/sda1)? Or the other way around?   EDIT     sudo ntfsfix /dev/sdb2 returns:  Mounting volume... NTFS signature is missing. FAILED Attempting to correct errors... NTFS signature is missing. FAILED Failed to startup volume: Invalid argument NTFS signature is missing. Trying the alternate boot sector Unrecoverable error Volume is corrupt. You should run chkdsk. Connectedness in the Quotient Space Exclude lstinputlisting I want to save paper when I print my LaTeX file. That's why I want to hide all my code, inserted wtih lstinputlisting{}  I already know how to exclude tables and images or math but the lstinputlisting{} is a problem.   Hope someone can help me  \usepackage{comment} \excludecomment{figure} \let\endfigure\relax \excludecomment{table} \let\endtable\relax \excludecomment{align*} \let\endalign\relax \excludecomment{lstlisting} \let\endlstlisting\relax   edit: added lstlisting Collapsible fieldsets error for previous dates How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$ If $A,B$ non empty, upper bounded sets and $A+B=\{a+b\mid a\in A, b\in B\}$, how can I prove that $\sup(A+B)=\sup A+\sup B$? I don't know so much about coordinate systems...  In my office we use to deal with spatial data coming from archaeological sites. Each site has its own x-y-z coordinate system (GCS). Three simple ortogonal cartesian axis. In the last years we have been managing this spatial data through GIS software (ArcGIS), without using specific coordinate system (just leave it as "undefined")  I'd like to know if there exisits any GCS designed to deal with such datasets using simple cartesian orthogonal axis, without grid distortions of the typical GCS. In addition, I'd like to know if this system is suitable for using it in an online mapping application.  By the way, we manage 2D (ArcMap) and 3D (ArcScene) environments and work with "mm" as length base unit.   If such a thing doesn't exists, maybe someone knows how to create it. How to redirect STDIN of background process? In my Ubuntu, i run java application in background. I use bash script to run it and now it looks like:  nohup java -jar app.jar &amp; exit 0   The problem that i want to be able to write an input string to my application, without making it foreground, from different terminals/sessions. Something like  echo "mytext" &gt; /appdir/in   How should i change my script? What is wrong with this fake proof $e^i = 1$? $$e^{i} = e^{i2\pi/2\pi} = (e^{2\pi i})^{1/(2\pi)} = 1^{1/(2\pi )} = 1$$  Obviously, one of my algebraic manipulations is not valid. I made a hair particle system and set the Dupli Group to a group of 3 objects. Each of the 3 objects has:   it's origin set to be touching the XY plane (on layer 2) it's Scale applied to 1 and it's Rotation applied to 0     I am trying to get each of the objects to sit directly on top of the ground, but instead, they are centered in the plane, half above the plane and half below the plane:      What am I doing wrong? Here is . Spice containers purchase  I'm planning on upgrading my spice storage. Reading some advice online (e.g. , and ) I came to the conclusion that spice containers should:   Not be exposed to direct sunlight and high temperatures Be airtight   Which means that either you store it inside of some closed cupboard/wardrobe/room or you have containers which do block light and are in a relatively shady place. And the containers need to be airtight.  Available solutions  I've been browsing for some containers available online in my country and the 2 most sensible options I've seen are these:       The problem  The first one is hermetic (it has some rubber around the lid) but it's clear glass. The other one does not have the rubber, just a regular twist-off lid, but it's amber glass.  It'll be hard for me to find any space inside of cupboards to store all of my spices (I need at least 30), so I'd rather buy amber glass container, which I believe will effectively block the sunlight, even when kept on the counter. But I can't find any hermetic amber-glass containers, only ones with regular lid.  The question  Is that regular twist-off lid enough to keep spices airtight and fresh? Or should I focus on buying a hermetic container (like the one in clear glass). I could then for example paint them black to block the sunlight. jQuery 1.9 checkbox not checked second time after once it unchecked SharePoint search not showing any results when searching partial name such as "frank" I have search service application configured.  Suppose my first name is "frankmartin" (no spaces)  When I search "frankmartin" then it displays search results in both "People" and "Site" search. But when I search "frank" it doesn't display any search result. Why is that?  EDIT  I am not using advanced search and have made this search results page using those search web parts which you can add in page to display results. XGBoost Loss function Approximation With Taylor Expansion I wanted to remove and reinstall the software-center package.  I removed it, but now I can't reinstall.  I tried these commands without success:  sudo apt-get update sudo apt-get install software-center   How can I reinstall software-center?    When I performed the install command this is what I got:  $ sudo apt-get install software-center Reading package lists... Done Building dependency tree        Reading state information... Done Package software-center is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'software-center' has no installation candidate Why doesn't grep using pipe work here? I know that there is no vector space having precisely $6$ elements. Does every set have a group structure? What exactly is voltage? Bit of a strange question, but what is it? My physics teacher said it was kind of like a "push" that pushes electrons around the circuit. Can I have a more complex explanation? Any help is much appreciated. Determinant of a block lower triangular matrix