Center Equation
center align equation in ‎\documentclass[11pt,twoside,fleqn]{book}‎
Isometric Embedding of a separable Banach Space into $\ell^{\infty}$ Finding total after percentage has been used? Tried my best with the title. Ok, earlier while I was on break from work (I have low level math, and want to be more fond of mathematics)  I work retail, and 20% of taxes are taken out, and I am wanting to find out how much I made before 20% is taken out.  So I did some scribbling, and this is without googling so please be gentle. but lets say I make 2000 dollars per paycheck, so to see how much money I get after taxes I do 2000 * .8 which gives me 1600. I can also do 2000 * .2 which gives me 400 and then do 2000 - 400 (imo I don't like this way since I have a extra unnecessary step)  Anyways, I was pondering how to reverse that to have the answer be 2000, and what I did was 1600 * 1.20 (120%) which gave me 1920, and I thought that is odd so I did 1600 * 1.25 and answer was 2000 exact.  My question is why did I have to add extra 5% (25%) to get my answer? I am sure I did something wrong, and I fairly confident the formula I am using is a big no no.  edit; wow thank you all for your detailed answers. I am starting to like mathematics more and more. What is the best technique for long-exposure photography in good light? Is it possible to recover an email that has been clicked "delete forever" in the trash folder? Is it possible to recover an email that has been clicked on "delete forever" in the trash folder? I have accidentally clicked delete forever for an email but now I need to recover it. How to ask "If you have any problem then ask me" in polite manner Why is the sun brighter in Australia compared to parts of Asia? What is the best way to dump entire objects to a log in C#? So for viewing a current object's state at runtime, I really like what the Visual Studio Immediate window gives me.  Just doing a simple  ? objectname   Will give me a nicely formatted 'dump' of the object.    Is there an easy way to do this in code, so I can do something similar when logging? Weird line in my mirrored mesh I flagged a post today, typed out a fairly thorough explanation, clicked the button... and got told that I'd already flagged this post (for something else, which I'd forgotten about) so this flag wasn't allowed.  (This happens if the first flag is still active.)  The dialogue with my explanation was gone at this point, so if I wanted to communicate with the moderators about that, I was going to have to start over.  (In case you're wondering how this could happen, one flag was related to the post itself and one was related to the user -- there being no way to flag a user directly, you have to hang it off of a post.  But I've also seen this with cases where the first flag hangs around unhandled for a week or two and I've forgotten about it.)  Since the system is going to detect that I've already flagged a post and reject a second flag, can it do that after I click the "flag" link instead of waiting until the end of the process?  (Or gray out the link so I can't click it in the first place?)  2015-12-18: someone suggested to me in chat today that this had been implemented, so I tested again.  The behavior has not changed: I flagged a post using "other", then flagged it again (also "other") before the first flag was handled, and the flag was rejected only after I'd typed the message.  (I did this on a site where I'm a moderator so I could then clean up after myself.) Add and remove update channels in an easy terminal way I know there is a GUI in Ubuntu Software &amp; Updates to enable the update channels   updates proposed backports security   as shown in this screenshot:    I am looking for an easy way to do this from within a terminal using commands such as    sudo apt-add-update enable updates sudo apt-add-update enable proposed sudo apt-add-update enable backports sudo apt-add-update enable security  sudo apt-add-update disable updates sudo apt-add-update disable proposed sudo apt-add-update disable backports sudo apt-add-update disable security   and an additional thing  sudo apt-add-update enable default  sudo apt-add-update disable default     Some examples for a better understanding   An empty sources.list   cat /etc/apt/sources.list  &lt;empty&gt;  sudo apt-add-update enable security  &lt;empty&gt;   One enabled repository (main)   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security main   Two or more enabled repositories in one or two lines   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe   or   deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe   or  deb http://archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security main deb http://archive.ubuntu.com/ubuntu wily universe deb http://archive.ubuntu.com/ubuntu wily-security universe   With deb-src entries   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe deb-src http://archive.ubuntu.com/ubuntu wily main universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb-src http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe deb-src http://archive.ubuntu.com/ubuntu wily-security main universe   With inactive deb-src entries   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe # deb-src http://archive.ubuntu.com/ubuntu wily main universe  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe # deb-src http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu wily-security main universe   The default thing    cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily-security universe  sudo apt-add-update enable default  deb http://archive.ubuntu.com/ubuntu wily universe deb http://archive.ubuntu.com/ubuntu wily-security universe   Only one entry and the disable action   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily-security universe  sudo apt-add-update disable security  &lt;empty&gt;   Different or the same servers for different or the samerepositories, respect each server   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily universe deb http://us.archive.ubuntu.com/ubuntu wily main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily universe deb http://us.archive.ubuntu.com/ubuntu wily main deb http://archive.ubuntu.com/ubuntu wily-security universe deb http://us.archive.ubuntu.com/ubuntu wily-security main   Different Ubuntu releases for different repositories, respect each release   cat /etc/apt/sources.list  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu trusty main  sudo apt-add-update enable security  deb http://archive.ubuntu.com/ubuntu wily main universe deb http://archive.ubuntu.com/ubuntu trusty main deb http://archive.ubuntu.com/ubuntu wily-security main universe deb http://archive.ubuntu.com/ubuntu trusty-security main   PPAs or other package sources (not-Canonical)  in the sources.list?  Ignore! Don't change the protocols, e.g. https, http, tor, ... How to add fonts in LibreOffice writer I want to add nepali fonts like kantipur in Ubuntu 12.04.How can I do this. Where to put my code: plugin or functions.php? RegEx for matching UK Postcodes How would one write object-oriented code in C? How to generate XML file dynamically using PHP? I don't know if this is a well-known fact, but I have observed that every number, no matter how large, that is equally divided by $9$, will equal $9$ if you add all the numbers it is made from until there is $1$ digit. A quick example of what I mean:  $9*99 = 891$ $8+9+1 = 18$ $1+8 = 9$  This works even with really long numbers like $4376331$ Why is that? This doesn't work with any other number. Similarly for $11$ and alternating digits sums. No sound in Ubuntu except at log in I installed Ubuntu 12.04 a month ago and am using it till now. I failed to notice that all this time there was no sound at all while running Ubuntu, even while playing a game in Wine. The weird thing is that only the startup sound comes when I log in (Indian/African drum tone), then comes the utter silence.  I tested both Digital Output (S/PDIF) and the speakers in the sound settings but can hear nothing.  Any help? EU flight compensation distance for connecting flight I recently had a flight from Valencia to London, going through Düsseldorf, cancelled. According to EU regulations there are different levels of compensation for flights below and above 1500 km in distance. I assume that this distance refers to start and end airport regardless of connection. Is this the case? I haven't found a proper definition online. Here, it would make a difference as VLC to LHR is around 1350 km, but the complete itinerary is above the 1500 km threshold. 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! $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit. Show $(z_n)_{n\in \mathbb{N}}$ converges to the same limit. $(z_n)_{n\in \mathbb{N}}$ is a complex valued sequence such that subsequences $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit.  How could I show that the sequence $(z_n)_{n\in \mathbb{N}}$ converges to the same limit using $\epsilon$, $N$ definition?    For every $\epsilon &gt;0$,  $|z_{2n}-l|&lt;\epsilon$ whenever $n&gt;N_1$, and   $|z_{2n+1}-l|&lt;\epsilon$ whenever $n&gt;N_2$.  We want to show that for every $\epsilon &gt;0$, there exists $N$ such that $|z_{n}-l|&lt;\epsilon$ whenever $n&gt;N$. I tried something like  $|z_{n}-l|\le|z_n-z_{2n}|+|z_{2n}-l|$ but wasn't sure what to do next