I just noticed that addition.   Searching for posts by author does not need the brackets [], and can be clearer as to what "1234" is. A new user may think 1234 is a username example. Tag guideline can be clearer, for example: [tag-name].
There's a new popup helping you with searching, but one of the hints is wrong:    Searching for  will return answers as well as questions, and it's not the number of (up/down)votes which counts, it's the score. Better would be "posts with a score of 3 or higher" or "questions and answers with a score of 3 or higher".
Generalized mean value theorem I know and understand the mean value theorem. But at the moment I don't have the intuition to understand the generalized mean value theorem     If $f$ and $g$ are continuous on the closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, then there exists a point $c\in(a,b)$ where$$[f(b)-f(a)]g'(c)=[g(b)-g(a)]f'(c).$$If $g'$ is never zero on $(a,b)$, then the conclusion can be stated as$$\frac{f'(c)}{g'(c)}=\frac{f(b)-f(a)}{g(b)-g(a)}.$$   What is the intuition? And how can you prove this (generally) ? How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic? While reading a book, I came across the word I'd've, as in:     I'd've argued against it.   While it was obvious what it meant, it left me puzzled. Is I'd've a proper word? Network interface name changes after update to 15.10 - udev changes I updated a virtual machine running Ubuntu server 15.04 to the just released new stable 15.10.  There were no apparent problems, but after reboot the machine lost its network connection. lspci showed the correct card and lsmod proved that the driver had been loaded.  Hints about editing or removing /etc/udev/rules.d/70-persistent-net.rules did not succeed (still no network, no new file), the famous /lib/udev/write_net_rules did not even exist.  I don't have much clue regarding udev and systemd, so it took me some time to find in /sys/class/net that the network interface name changed. It became ens32, which was renamed from eth0. After I changed /etc/network/interfaces network communication was enabled again.  But - why does this happen at all? And if it happens, shouldn't the interfaces file be updated automatically?  Now that I deleted the virtual network card and created another one, eth0 becomes eno16777728, which is not so, uhm, nice.  Should this behaviour (at least that of the upgrade procedure) be reported as a bug?  Furthermore, is /etc/udev/rules.d/70-persistent-net.rules obsolete now? And (although only partly related) what about /etc/udev/rules.d/70-persistent-cd.rules?)  Edit - additional question (after accepted answer) The dependency of /etc/network/interfaces from the actual interface name bothered me. I tried a new installation of *ubuntu in another virtual machine. To my surprise, /etc/network/interfaces contained a reference to the loopback device only. However, with my original VM this change prevented the network to come up. So what else do I need to change?  Edit Well, from another test I found that a new Ubuntu Server has the network interface card in /etc/network/interfaces, while XUbuntu has not. Maybe it is using network-manager or something else. I am reading through Folland's Real Analysis: Modern Techniques and Their Applications, and they have the following proposition and proof:     Proposition: If $\{f_{j}\}$ is a sequence of $\bar{\mathbb{R}}$- valued measurable functions on $(X, \mathcal{M})$, then the functions:      $$g_{1}(x)=\sup_{j} f_{j}(x)$$ $$g_{2}(x)=\inf_{j} f_{j}(x)$$ are   measurable.       Proof:      We have       $$g_{1}^{-1}((a,\infty])= \bigcup_{j=1}^{\infty}  f_{j}^{-1}((a,\infty])$$ $$g_{2}^{-1}([-\infty,a))=  \bigcup_{j=1}^{\infty} f_{j}^{-1}([-\infty,a))$$      Where the result follows from the fact that $g_{1}^{-1}((a,\infty])\in  \mathcal{M}$ for all $a \in \mathbb{R} \iff g$ is measurable, and   $g_{2}^{-1}([-\infty,a))\in \mathcal{M}$ for all $a \in \mathbb{R}  \iff g$ is measurable.   I understand the last part of the proof, but how do we know $g_{1}^{-1}((a,\infty])= \bigcup_{j=1}^{\infty}f_{j}^{-1}((a,\infty])$ and $g_{2}^{-1}([-\infty,a))=\bigcup_{j=1}^{\infty} f_{j}^{-1}([-\infty,a))$? I would appreciate any help with this. I have a few satellites and stations orbiting my planets, but I'd like to add onto them. I've seen numerous videos on using docking clamps to attach my new ship to the existing station, but can I do that on a part-by-part basis? For example, I take an extra fuel tank up there, can I attach just the tank to my station, then send my vessel back to Kerbin? I'm not talking about refueling, but rather transferring individual parts from my ship to the station in orbit.  I'd prefer to not have to use an unmanned probe and jettison everything but the desired part in space after docking if possible, but if that's the only way I guess I don't have a choice. Can I use my Windows 7 license in a dual-boot configuration? Possible Duplicate:          I've purchased a retail license of Windows 7 Ultimate for my machine at home.  I'm thinking of creating a dual-boot install:   64-bit install for work apps (need the RAM for virtual machines and RAMDisk) 32-bit install for entertainment apps (Media Centre, games, etc)   How does retail licensing work in such situations? Can I activate the same license on both installations?  Edit:  I would like to add that I want to have separate partitions for work and play. By considering:  $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^1}{n^{2}} = \frac 1 2$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^2}{n^{3}} = \frac 1 3$$ $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^3}{n^{4}} = \frac 1 4$$  Determine if this is true: $$\lim_{n\to\infty}\frac{\sum_{k=1}^n k^m}{n^{m+1}} = \frac 1 {{m+1}}$$  If it is, prove it.  If it is not, evaluate $\lim\limits_{n\to\infty}\frac{\sum_{k=1}^n k^m}{{m+1}}$. equal size numerator and denominator I am trying to size the numerator and denominator of the below equation so that they are equal in size.  I have not had much luck suggestions are appreciated.  \begin{equation} \sum_{i=1}^{n} \frac{\frac{cf_{n}}{(1+i)^n}} {\displaystyle\sum_{i=1}^{n}\frac{cf_n}{(1+i)^n}} , n_{i} \end{equation} Let $G$ be a finite group of order $n\ge2$. Which of the following statements are true? a. There always exists an injective homomorphism from $G$ into $S_n$. b. There always exists an injective homomorphism from $G$ into $S_m$ for some $m\lt n$. c. There always exists an injective homomorphism from $G$ into $GL_n(R)$.  I think b. is right (don't know how to prove though). I also think that c. is false. But not sure. How long can I run a water pump which requires 12V and 50W from a 12V, 40Ah, 400A car battery?  Can you explain how this was calculated? Batch file to create Folder based on Date and Copy Files from One Location to Another Location? How to increase difficulty in Dungeon World I've been GMing for a couple of sessions now and I'm still struggling at making encounters or situations more difficult. I will describe dangerous situations and encounters in fiction but the mechanics make it too easy for my players to succeed.  For instance no matter how big I describe the Troll, if the fighter of the party charges him and swing his sword, roll+2 for Hack and slash, he'll easily hit the troll. Almost 40% chance to hit without consequences. Placing the object of an infinitive before it instead of after it I recently upgraded from QGIS 3.2 to 3.4 using the standalone installer (Windows 64 bit), and uninstalling 3.2 beforehand.  When I open 3.4 it goes the background behind all my other open programs and clicking its icon on the taskbar does nothing, nor does Alt-Tab.  To use QGIS I have to minimize all my other open programs.    Is this a Windows issue, a QGIS issue, or something else entirely? Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ($F=ma$) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction? Don't you think people need to know what they did wrong exactly so they can fix it and get unbanned from asking questions or posting answers? How do I write this matrix as a product of elementary row matrices. \begin{pmatrix}3&amp;-1&amp;3\\ -2&amp;3&amp;2\\ 1&amp;-3&amp;1\end{pmatrix}  Any help would be greatly appreciated!  I have done this before with other matrices, yet this one is bringing me trouble. I have spent too long on this as I believe it should be easy and yet my answers are always wrong. What Do you do after you get the identity matrix?  What I am doing: So I first row reduce it to the identity matrix:   I first switch $R_1$ and $R_3$ Then $R_3-3R_1$ then $R_2+2R_1$ then $-1/3R_2$ then $R_3-8R_2$ then $R_2-2R_1$ then $3/32R_3$ then $R_1+3R_3$ and finally $R_2+4/3R_3$   I know there is many possible ways to get this too the identity matrix but this worked for me. I then apply all of the above steps to identity matrices and multiply them together to check my work but it never works out to be the original matrix so I am forced to believe something is wrong. What is the purpose of wrapping whole Javascript files in anonymous functions like “(function(){ … })()”? How to loop over the lines of a file?