If L and M are algebraic over K then so is LM
$M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions? Write down the set of distinct solutions and prove your list is complete. $x$ and $y$ are positive integers.  I have rewritten it as $\frac{(x+y)}{xy} = \frac1p$, but I don't understand where to go from here? How can I set default terminal used in Unity? How can I set the default terminal used in Unity?  I would like to use the Ctrl+Alt+T hotkey to start a non-default terminal. The default terminal is gnome-terminal.   Where can I change the default terminal value? How do I choose a macro lens for a Canon APS-C camera? I have an iPhone 4s with iOS7 and somehow I see iCloud music which I haven't downloaded yet on my iOS device. How can I get rid of these, I do not need to see them. Edit Mode buttons for selecting vertices and edges vanished When I am in Edit Mode for my project, the Mesh Select Mode buttons have disappeared!  I loaded the default project and the buttons are where they are supposed to be; the issue is only in my project. In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. Zip all files in directory? Is there a way to zip all files in a given directory with the zip command? I've heard of using *.*, but I want it to work for extensionless files, too. What is the reason behind the multiple Spider-Man reboots? Do not enumerate a section, but add it into table of contents How do I rid of number of a section in the way that it still would be in the table of contents.  If I use   ... \section{SN1} ...   then I see this section name in table of contents as   1 SN1  2 SN2  3 SN3  ...   If I use   \section*{SN}   I don't see it in the content:   1 SN2  2 SN3   How to get in content just   SN1  1 SN2  2 SN3   ? Change Text Color in Blender Game Engine? I want to change the color of some text in my game. I've tried adding materials, but whenever I press P to play the game, the text stays the same white color. Any ideas? Travelling without a visa after passport was stolen Similar to Lifepod 1993, but not it Rsync filter: copying one pattern only I am trying to create a directory that will house all and only my PDFs compiled from LaTeX. I like keeping each project in a separate folder, all housed in a big folder called LaTeX. So I tried running:  rsync -avn *.pdf ~/LaTeX/ ~/Output/   which should find all the pdfs in ~/LaTeX/ and transfer them to the output folder. This doesn't work. It tells me it's found no matches for "*.pdf". If I leave out this filter, the command lists all the files in all the project folders under LaTeX. So it's a problem with the *.pdf filter. I tried replacing ~/ with the full path to my home directory, but that didn't have an effect.  I'm, using zsh. I tried doing the same thing in bash and even with the filter that listed every single file in every subdirectory... What's going on here?  Why isn't rsync understanding my pdf only filter?    OK. So update: No I'm trying  rsync -avn --include="*/" --include="*.pdf" LaTeX/ Output/   And this gives me the whole file list. I guess because everything matches the first pattern... How to keep application running after closing the terminal? "physical block size is 2048 bytes, but Linux says it is 512" when formatting USB - How to create a bootable USB without this error I was using:  dd  if=/path/to/my/ubuntuiso/ubuntu.iso  of=/dev/sdb1  bs=4M  &amp;&amp;  sync   In order to create bootable Ubuntu USB drives on older Ubuntu versions. It was working perfectly. Sometimes I used the Startup Disk Creator program, which  worked well.  But when I use the same methods on Ubuntu 16.04 LTS, I get some warnings while formatting it afterwards.   The installation media works as expected, but when I try to format that USB stick after my work is done, I get the following warning :    The partitioning of that Pendrive looks strange :    And it also shows my 16GB pendrive as 64GB.  After struggling a lot with Gparted, I will somehow format it. But Why is it happening like this ?? Is there any better methods of creating bootable Ubuntu in 16.04 ?  EDIT : there is a related question . But my question is not about how to format it properly. My question is "How to create a bootable USB without that errors." &amp; "Wht are the causes of that error" What settings should I be using to shoot "Supermoon"? Where does matter go after reaching singularity in uncharged black holes? I am a layman in physics and just read about black holes on the internet. I read that matter encounters geodesic incompleteness in the singularity in an uncharged black hole.  I heard an analogy of geodesic incompleteness as a straight line on a paper reach a hole on the paper, so it cannot continue. But in this analogy, isn't the straight line possible to continue into 3D (continue down the paper)? So, if matter reaches the singularity, is it possible too (to reach another dimension)?   I also heard that the matter is annihilated when reaching the singularity, does it mean it disappear from this world, and violates conservation of energy? I know enough amount of set theory and logic to study grad-level math. However, I don't know more advanced set theory and logic, such as the ones on Kunen's or Shoenfield's texts. Although it's good to learn such advanced topics, I may not have enough time to do so, since I will probably put my emphasis on algebra, analysis or geometry as well as mathematical physics.   Although how much set theory and logic I should learn is totally up to what sort of analysis, algebra or geometry I will study, I want to know how much of them typical competitive algebraists/analysts/geometers know. If you are one of them, how much do you know? I am using a tikzpicture for plotting. the values I want to plot are typical (X,Y) pairs. The x-value is an uninteresting id-value. I want to order the bins ascending/descending according to the y-value, but how do I do that? The figure seems to automatically take the x-values for ordering, how can I override that? (I am not particularly fixed to tikzpicture - its just the first thing that actually worked and displayed the plot....) Following minimal-working example, how could I achieve a reordering according to the y-value?  \documentclass{article} \usepackage[english]{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{relsize} \usepackage{times} \usepackage{url} \usepackage{latexsym} \usepackage{graphicx} \usepackage{colortbl} \usepackage{color} \usepackage{caption} \usepackage{pgfplots, pgfplotstable} \usetikzlibrary{arrows} \usepackage{amsmath} \usepackage{multirow} \usepackage{booktabs}  \usepackage{filecontents} \definecolor{OgAns}{rgb}{0, 0.8, 0.4}  \begin{filecontents}{testdata.dat} 1   30 2   44 4   26 3   39 \end{filecontents}  \begin{document} \begin{figure} \begin{tikzpicture}         \begin{axis}[                ybar stacked,             ymin=0,             ymax=100,             bar width=5pt,             legend style={at={(0.35, -0.4)},anchor=south west},             legend columns=-1                       ]           \addplot[ybar,fill=OgAns]  file {testdata.dat};          \end{axis}     \end{tikzpicture} \end{figure}   \end{document} Why do we need to use `int main` and not `void main` in C++? Why do we need to use int main and not void main in C++?