I am doing the following exercise from my functional analysis course.     Prove that $$d(\{x_n\},\{y_n\}):=\sum_{n\geq 1} 2^{-n} \dfrac{|x_n-y_n|}{1+|x_n-y_n|}$$   is a metric on $\mathbf{R}^{\mathbf{N}}$.   Is this some kind of known norm? I tried looking on the internet and I found similar expressions with the name F-norm. Any information on this norm is helpful.  Currently, I am stuck proving the triangle inequality for this metric. This must follow from the triangle inequality for $|\cdot|$.   I think it is equivalent to proving that   $$\frac{|x_n-z_n|}{1+|x_n-z_n|}\leq \frac{|x_n-y_n|}{1+|x_n-y_n|}+\frac{|y_n-z_n|}{1+|y_n-z_n|},$$  which is in turn equivalent to   $$1+\frac{1}{1+|x_n-z_n|}\geq \frac{1}{1+|x_n-y_n|}+\frac{1}{1+|y_n-z_n|}.$$  Reformulating, I am trying to prove that if $a,b,c\geq 0$ and $a\leq b+c$, then $1+\frac{1}{1+a}\geq \frac{1}{1+b}+\frac{1}{1+c}$. I am not really good at inequalities, can someone give a hint?
I am pretty sure that this is such a stupid, stupid question, but how do you prove that $d_2(x,y)={|x-y|\over {1+|x-y|}}$ satisfying the third condition to be a metric, which is the triangle inequality.   I know that I should really be able to do this, but I just can't, I keep seeing a contradiction. Please help me.
Eclipse menus are cut off or don't show I'm using Ubuntu 13.10 (with JDK 1.7.0_45).  I've downloaded and uncompressed Eclipse Kepler for Java EE Developers.  The software menus are messed up. I didn't notice similar problems in other software.  When I click any menu in Eclipse, the drop-down seems to be "cut". Sometimes the drop-down shows, but the options are invisible.  I tried Eclipse Indigo, but the same problem occurs. Why is it so difficult to pull an immersed mug out of the water? Suppose I put a mug in the water and then tilt it so that the water gets inside. It then floats due to buoyant force. But if I try to pull it out then a lot of force is needed. That's due to suction? What exactly happens at the moment when the force I apply is enough to pull the mug out? And what causes the loud pop sound when that happens? When I upgrade from one version of Ubuntu to the next, the upgrade tool rightly disables all my PPAs, so that software compiled for or otherwise tied to the old version of Ubuntu does not interfere with the new version that I just upgraded to.  Is there any way to automatically re-enable and update any PPAs that provide packages for the new version of Ubuntu? For example, suppose I'm currently running Maverick, and I have two PPAs enabled, "foo" and "bar". Suppose that "foo" provides packages for both Maverick and Natty, while "bar" provides packages for Natty only. Is there a tool I could run after updating to Natty that would re-enable my "foo" PPA and update it to point to the Natty packages, while leaving the "bar" PPA disabled? Why is the Cantor function not absolutely continuous? Is there an easy way to see that the Cantor function is not absolutely continuous that directly uses the definition of absolutely continuous? Why do I not see evidence of discrete energy in the spectrum? The electromagnet spectrum looks to be continuous, yet energy is discrete. Shouldn't one see evidence of the electron's "quantum leap"? What's going on?     Moderator, please size my photo. Thank you. Is it possible to play FIFA 2015, 4v4 on 2 Consoles? I've the following situation: My friends and I, we're 8 in total, want to play Fifa 15 4v4. I know that the Playstation 4 just supports 4 controllers and thats why we think about a 2 console + 2 TV's setup, so 4 players per console.   So my question is: Is it possible or is there a game mode available were we could play such a setup?  Update: After I got the first answer I've to add that I know that the only way to play on 2 consoles would be through the psn online features. So we did not plan to play on Lan. We just want to sit in the same room with 2 consoles and play against each other over psn. Why does Ubuntu 12.10 not detect my Win7 partition? I'm trying to install Ubuntu 12.10 alongside Windows 7 on my ASUS laptop and I'm new to all of this.   I'm using  the Ubuntu 12.10 64-bit ISO burned onto a CD.  The first time I tried to install it, Ubuntu said it did not detect any other OS, which meant I only had 4 options:   Erase disk and install Ubuntu (I don't want to do this) Encrypt new Ubuntu. Use LVM. Something else.   If I choose the Something else option, it brings me to the partition menu and says that I have 1 disk with free space of 750516Mb (750Gb), but that's not true because I have Windows 7.  I've already read through several questions and people have mentioned that you could only have 4 primary partitions. So I got hold of partition magic and removed my D: and E:, leaving me with primary C: partition and System reserved partition and a lot of unallocated space.  I restarted the laptop several times and booted the CD again and I got exactly the same as I did previously.  How do fix this problem and install Ubuntu alongside Windows 7?  EDIT 1  Here are my results for   sudo fdisk -l; echo; sudo parted -l; echo; mount; echo; df -h   WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 750.2 GB, 750156374016 bytes 255 heads, 63 sectors/track, 91201 cylinders, total 1465149168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x90050371     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048      206847      102400    7  HPFS/NTFS/exFAT /dev/sda2          206848   146368214    73080683+   7  HPFS/NTFS/exFAT  Warning: /dev/sda contains GPT signatures, indicating that it has a GPT table. However, it does not have a valid fake msdos partition table, as it should. Perhaps it was corrupted -- possibly by a program that doesn't understand GPT partition tables.  Or perhaps you deleted the GPT table, and are now using an msdos partition table.  Is this a GPT partition table? Yes/No?     After selecting YES  Yes/No? yes                                                                Error: The backup GPT table is corrupt, but the primary appears OK, so that will be used. OK/Cancel? Using Green's identity to show that a harmonic function with zero boundary values is identically zero I am confused how to do this question. I need to use Green's first identity and if $\nabla(f)=0$ then $f$ is constant on $\Omega$ since $\Omega$ is path connected.  I have subbed in the information into green's identity but I don't get anything useful.  $$\iiint_\Omega \nabla f\cdot \nabla g \,dV =\iint_{\partial\Omega} f\nabla g\cdot n \,dA - \iiint_\Omega f\cdot \Delta g \,dV$$   We get:  $$\iiint_\Omega \nabla f\cdot \nabla g \,dV =-\iiint_\Omega f\cdot \Delta g \,dV$$   $$\iiint_\Omega \nabla. (f \nabla g) \,dV =0$$ $$\iint_{\partial\Omega} f\nabla g\cdot n \,dA=0$$ Google page title not matching html  tag Did this character even qualify for being Azor Ahai or The One Who Was Promised? In the books and to some degree in the show as well there is a prophesy about the legendary figure Azor Ahai. But in the latest Game of Thrones episode (S08E03) we see Arya      killing the Night King.   However in a  we discussed​ all possible candidates but nobody thought about Arya. Does she even fulfill the prophecy? If she does, how? Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$ White's test for heteroskedasticity in R I am trying to estimate heteroskedasticity in R. I had Eviews available in my college's lab but not at home. I have been trying to use "het.test" package and whites.htest but the value that I get is different from what I get in Eviews. According to the author of the package, it is meant to do the same test as is done in Eviews.   My model looks like A~B+C. Kindly guide me what I am doing wrong.   I 1st run ols for equation A~B+C, after getting results, I clicked View&gt;Residual diagnostics&gt;Heteroscadicity tests&gt;White's (with Include white cross terms) and then Press ok. The result i got was Prob. F(5,27) = 0.2948.   For R, i tried code at this link [this link][1], here is the edited code that i used.  library(vars)  library(het.test) dataset &lt;- data.frame(A,B,C))  model1 &lt;- VAR(dataset, p = 1)  whites.htest(model1)   This gave me value of 0.63.  I tried searching this forum but none question seemed related. I am not a programmer not statistician so please pardon my ignorance. How to get the insert ID in JDBC? Converting LiDAR files from LAZ to LAS format I'm trying to convert LiDAR files from the LAZ format (the compressed version) into LAS (the uncompressed version) using  software.   However, I am not really sure how it works. I created a new output folder as I entered in the app interface, but it is totally empty.  I also had tried the following code in the command prompt window:   D:\LiDAR\Laszip\laszip.exe *.laz    and got a message saying 'no input specified'.  In my folder, there are about 100-ish.laz files as well as one imu.laz. Any suggestions? How do I detach a process from Terminal, entirely? I use Tilda (drop-down terminal) on Ubuntu as my "command central" - pretty much the way others might use GNOME Do, Quicksilver or Launchy.  However, I'm struggling with how to completely detach a process (e.g. Firefox) from the terminal it's been launched from - i.e. prevent that such a (non-)child process   is terminated when closing the originating terminal  "pollutes" the originating terminal via STDOUT/STDERR   For example, in order to start Vim in a "proper" terminal window, I have tried a simple script like the following:  exec gnome-terminal -e "vim $@" &amp;&gt; /dev/null &amp;   However, that still causes pollution (also, passing a file name doesn't seem to work). Pageblocktable to be rendered as table in PDF I have a VF code below where I am trying to display the related list of an object using  and  command. I am rendering this page as PDF , doing that in my PDF I am unable to see the content in a tabular format. How can I make the content appear in a table?      &lt;apex:pageBlockSection columns="1" title="TECHNICAL ASSESSMENT"&gt;          &lt;apex:repeat value="{!interviewSkillReviews}" var="interview"&gt;              &lt;table border="1" cellpadding="6"&gt;                 &lt;apex:pageblockTable value="{!interview.Skill_review__r}" var="skillreview"&gt;                      &lt;apex:column headerValue="Skill Name"&gt;                                                         &lt;apex:outputText value="{!skillreview.Skill__r.Name}"/&gt;                     &lt;/apex:column&gt;                 &lt;apex:column headerValue="Recommended Level"&gt;                     &lt;apex:outputText value="{!skillreview.Level__r.Name}"/&gt;                 &lt;/apex:column&gt;                  &lt;apex:column headerValue="Rating"&gt;                     &lt;apex:outputField value="{!skillreview.RatingCopy__c}" rendered="{!NOT(interviewerMode)}" /&gt;                     &lt;apex:selectList value="{!rating}" multiselect="false" size="1" rendered="{!interviewerMode}"&gt;                         &lt;apex:selectOption itemValue="1" itemLabel="1"/&gt;                         &lt;apex:selectOption itemValue="2" itemLabel="2"/&gt;                         &lt;apex:selectOption itemValue="3" itemLabel="3"/&gt;                         &lt;apex:selectOption itemValue="4" itemLabel="4"/&gt;                         &lt;apex:selectOption itemValue="5" itemLabel="5"/&gt;                     &lt;/apex:selectList&gt;                 &lt;/apex:column&gt;                  &lt;apex:column headerValue="Rating Level Description"&gt;                     &lt;apex:outputText value="{!skillreview.Skill_Level_Description__c}"/&gt;                 &lt;/apex:column&gt;               &lt;/apex:pageblockTable&gt;         &lt;/table&gt;      &lt;/apex:repeat&gt; &lt;/apex:pageBlockSection&gt;   I tried using &lt;table&gt; command of HTML but I just get a border around the pageblocktable.    Example of table look and feel: How can I get ssh-agent working over ssh and in tmux (on OS X)? I have a private key set up for my github account, the passphrase to which is, I believe, stored in OS X's keychain. I certainly don't have to type it in when I open a terminal window and enter ssh git@github.com.  However, when I'm running bash over an ssh session, or locally inside a tmux session, I have to type in the passphrase every single time I attempt to ssh to github.   suggests that a similar problem exists with screen, but I don't really understand the issue well enough to fix it in tmux. There's also  which includes a fairly complicated solution, but for zsh.  EDIT:  In response to , from a local terminal I get the following output:  [~] $ echo $SSH_AUTH_SOCK /tmp/launch-S4HBD6/Listeners [~]  $ ssh-add -l 2048 [my key fingerprint] /Users/richie/.ssh/id_rsa (RSA) [~] $ typeset -p SSH_AUTH_SOCK declare -x SSH_AUTH_SOCK="/tmp/launch-S4HBD6/Listeners"   Whereas over ssh or in tmux I get:  [~] $ echo $SSH_AUTH_SOCK  [~] $ ssh-add -l Could not open a connection to your authentication agent. [~] $ typeset -p SSH_AUTH_SOCK bash: typeset: SSH_AUTH_SOCK: not found   echo $SSH_AGENT_PID returns nothing whatever shell I run it from. Strange object.ray_cast() behavior object.ray_cast() is not behaving as I would expect in Blender 2.77. I understand that it expects object local coordinates, but this problem happens when the object is not translated, rotated, or scaled.  If I edit the shape of the cube mesh without moving the cube, the results of ray_cast() seem plain wrong.  Steps to reproduce   Create a cube at 0,0,0 Move a vertex of the cube from 1,1,1 to 5,5,5 Create an empty called "src" at 2,2,2 Create an empty called "dst" at 2,2,6   Run this python  cb = bpy.data.objects['Cube'] src = bpy.data.objects['src'] dst = bpy.data.objects['dst'] hit, loc, norm, face = cb.ray_cast(src.location, dst.location) bpy.ops.object.empty_add(location = loc)   This is the result on my system. The new Empty created at the interesection point is selected:    The source and the destination are both at x = 2 and y = 2. The cube has a surface at x = 2 and y = 2. So why on earth is the intersection point at x = 2.22222, y = 2.22222? Where does Drupal store its content? I have been currently learning Drupal while trying to duplicate a Drupal application into CakePHP.  I have been looking at the  database tables to know where data is being stored so I can safely migrate any data or study how it is working.  I have researched and have come across questions like:     So far, I have only seen the title in my Drupal (7) installation.  What I have seen in my node revisions table for a recipe content type, which includes fields like, field_ingredients, field_instructions, field_description, field_preptime, field_cookingtime, just the title of the recipe. This is a sample record on my node_revision table.  nid   |  vid  |  title         |  log   | timestamp  | status | comment | promote  | sticky ------------------------------------------------------------------------------------------- 1     |  1    |  Awesome Sauce |        | 1369998600 | 1      | 2       | 1        | 0   As you can see I can only see the title. Where are the other field contents? Inverse metric in linearised gravity