Can every quadratic extension of $\mathbb{Q}$ be extended to a cyclic extension of degree 4?
A characterisation of quadratic extensions contained in cyclic extensions of degree 4
I would like to make a sum of all dropdown values into a label text box. I am using following formula, but I do not understand where am I going wrong. Can anyone assist? I have also added a screenshot if that helps anyhow. Note: scores is the table name the dropdown values feed from. Sum(scores, Dropdown3.Selected.Value + Dropdown3_1.Selected.Value + Dropdown3_2.Selected.Value) Typesetting linguistic rewrite rule I'm trying to (more or less) replicate this phonological rewrite rule:    I'm using the package , and what I manage to accomplish is this:  \documentclass{article} \usepackage{phonrule} \begin{document}  \phonc     {\phonfeat{$-$cnt\\ +hi}}     {[$\alpha$grv]}     {\oneof{%         \phonfeat{$-$cnt\\ $\alpha$grv}\phold\\         \phold\phonfeat{$-$cnt\\ $\alpha$vce}%     }}  \end{document}     My main problem here is what appears after the "when" slash:  (1) The package only provides a left curly bracket - how can I add a right one as well?  (2) The two options within the curly brackets are not well aligned. I think comparing the two pictures themselves says it better than what I could do with words. Self-Studying Measure Theory and Integration As the title says, I'm interested in reading about measure theory and integration theory on my own time, and was hoping for book recommendations, prerequisites, and things like that.  As for my background, I've taken introductory analysis, where we covered the "typical" subjects up until some theorems about differentiable functions.  I'm taking intermediate real analysis now; we talked about metric spaces in general for a while, but lately we've focused solely on $\mathbb{R}^n$. Now we're working towards a proof of the implicit function theorem in $\mathbb{R}^n$.  I haven't learned any of the theory behind Riemann integration, unfortunately. Is it important to be familiar with this first? Passing multiple commands to gnome-terminal from a script My bash-script is not run in a terminal, but opens a terminal at runtime to ask for user input (sudo password). I would like to tell the user in this terminal what the script is trying to do. First, here is my script:  #!/bin/bash #This should install: Qt Linguist, lrelease  #for Qt Linguist dpkg-query -l qt4-dev-tools if echo $? == 0; then  check1=1 fi  #for lrelease dpkg-query -l qt4-default if echo $? == 0; then  check2=1 fi  echo $check1 echo $check2  if [ $check1 = 1 ] &amp;&amp; [ $check2 = 1 ];then  gnome-terminal -x sudo apt-get install qt4-dev-tools qt4-default fi $SHELL   This opens a terminal with this:  [sudo] password for "username":    But I would like to have:  qt4-dev-tools and qt4-default are missing. Now trying to install. [sudo] password for "username":    How do I get this when starting the terminal with gnome-terminal -x? Proof for alternative definition of the derivative I read somewhere recently that you can define the derivative as follows:  $$f'(x) = \lim_{h, k \to 0^+} \frac{f(x +h) - f(x - k)}{h + k}$$   I have been trying to prove this for about 2 hours, and can't seem to get it done. How should I proceed?  Edit: Assume $f$ is differentiable for all $x \in (x - \delta, x + \delta)$ for some $\delta &gt; 0$. I know that atan2 gives me the absolute angle of any vector. But it doesn't give a value from 0 to 360 degrees. Instead, it gives a value (if I'm not mistaken), between 0 and 180, or between 0 and -180. For example, instead of giving angle 270, it will say -90.  This is a little confusing for me. Let me try to describe how I think this works, and please tell me if I'm correct. Actually, I'll draw it.    Is this correct? I'm having a little trouble understanding this. Thanks Why do same/opposite electric charges repel/attract each other, respectively? Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! Why L1 norm for sparse models Can't download any app from AppStore! I'm using iPhone 6s 16 GB. My storage isn't full but still I can't download anything. Every time I wanted to start a download it keeps telling:  app name* could not be download at this time What's a recommended alternative to Quickbooks pro? I've just installed Ubuntu to replace Windows. I can't seem to find a good alternative to  to run on Ubuntu. Any help would be appreciated. Generating list of manually installed packages and querying individual packages I'd like to get a list of packages installed manually by apt or aptitude and be able to find out whether a foobar package was installed manually or automatically. Is there any neat way of doing that from the command line? How do I know if a given food or ingredient I have is still good, or if I should discard it?  How can I best preserve a food or ingredient?     This broad question is intended as a "general reference" question to quickly answer many how long will food keep for? questions. Please feel free to edit this question to expand and clarify as needed. ́╗┐' is not recognized as an internal or external command When executing certain files (mainly batch) using PsExec I get these weird ́╗┐' symbols before my command. My initial thought was, that I were using wrong encoding, but after checking, I realized that all my files were using UTF-8. Ordinal dependent variable with continuous independent variables What's using up my disk space? My Vista 64 installation has drive C, a 150 GB hard drive.  I also has a 1.5 TB drive D.  My C drive has 12.3 GB free.  I don't know what's using up all the space.  There's almost 83 GB unaccounted for!!!  As per  question and  question, I downloaded  and .  WinDirStat, once I found the right options, tells me there's 82.9 GB of .  SpaceMonger, which has a particularly nice display of the data, tells me there's 82.3 GB "Unscanned", with 2 unscannable folders.  Where do I turn now?  Both tools roughly agree there's a large amount of data on my drive, but neither seem to be able to tell me what.  I've tried the standard approach; disk cleanup, remove hibernation file, set the virtual memory to the D drive instead of the C drive. I want to ask how to get id of element which was clicked by right clicking in open menu. I must know ID of this element to show only that history the element what was clicked fom open menu: Sometime in the 1970s (I think) I saw a really awful film set in a small town by a lake. The film opened with some people camping out in the woods. One of them was zipped up in a sleeping bag. Something (as yet unidentified) moved in between the sleeping camper and the camera, and we heard a "crunch." When the creature moved off, we saw that it had bitten the head off the camper, causing a fountain of blood to spout of of the neck. Far from being shocking or gory, it was so badly done as to be laughable.  The main story was that these huge and nasty mutated creatures were coming out of the lake and eating people. A local industrial company was under suspicion for poisoning the lake, but repeated water tests showed it to be clean.  In the end, someone had the idea of testing the water at the bottom of the lake, which revealed it to be heavily poisoned with mercury. As mercury is much heavier than water, it had sunk, so the previous tests (done from a small row boat) had missed it as they only sampled the water at the surface.  They got it all sorted out eventually, and the bad guys ended up in prison.  After the credits had rolled, and you thought it was all over, another monster reared up in front of the camera and roared. I think we were supposed to go "Oh no, it's not all over!" However, the few people stupid enough not to have left by now laughed at the ridiculous sight and left, shaking their heads wondering why they had bothered!  I have a morbid fascination to see it again. Anyone have any idea what it was called? Could I use a 1/2TB USB 2/3 external HDD with an XBox 360? How do I get the latest GIMP version available? I understand that there is a new version of the GIMP available, although it appears that the only way of doing this is by compiling from source :P  Is there another way of getting it, or if I have to compile can I do that through the terminal or better still; a GUI?