I'm reading a theorem about the order of a finite field:  Here is the proof:   At the end, the author said  It follows that $\mathbb{F}$ is a vector space over $\mathbb{F}_{p}$, implying that its size $q$ is equal to $p^{m}$ for some $m&gt;0$.  I do not understand how $\mathbb{F}$ is a vector space over $\mathbb{F}_{p}$ implies that its size $q$ is equal to $p^{m}$. Could you please elaborate on it?
Are there any galois fields which consist of product of two primes, as in $\mathrm{GF}(2\cdot 3) = \mathrm{GF}(6)$?
What happens when Wild Shape/Polymorph runs out in a space that's too small? What does a de Broglie wave look like? What does a  wave look like? Are de Broglie waves transverse or longitudinal?   Can they be polarized?    What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom?   What experimental evidence do we have that supports the detailed nature of a de Broglie wave?     I have always assumed that de Broglie waves were mathematically  identical to electromagnetic waves, but I just realized there is no basis for this assumption, and in fact it must be false, unless there is an analogue to both the magnetic and the electric components of the electromagnetic wave.  So what does a de Broglie wave "look like"? I'tm trying to show in SQLcmd window the results of these queries:  SELECT SYSDATETIME() AS "date";  PRINT 'EXTRAÍDO POR:' SELECT SUSER_NAME() AS "Owner"  PRINT 'PASSWORD SETTINGS'; exec xp_loginconfig;  PRINT 'PASSWORD SETTINGS'; select * from sys.sql_logins;   And using this command in SQLcmd:  sqlcmd -S myServer -i inputpath -s, -o outputPath(like C:\log.xls) -e   So the sqlcmd output the file and does not show nothing in sqlcmd screen. How can i print these "Print" commands in the sqlcmd screen? (command promt).  When I run it on SSMS works well, like:  (1 row affected) OWNER:  (1 row affected) PASSWORD SETTINGS  (8 rows affected) PASSWORD SETTINGS  I would like to show in the prompt command this, like in the SSMS.  Thanks! Bias and variance in leave-one-out vs K-fold cross validation How do  methods compare in terms of model variance and bias?   My question is partly motivated by this thread: . The answer there suggests that models learned with leave-one-out cross-validation have higher variance than those learned with regular $K$-fold cross-validation, making leave-one-out CV a worse choice.  However, my intuition tells me that in leave-one-out CV one should see relatively lower variance between models than in the $K$-fold CV, since we are only shifting one data point across folds and therefore the training sets between folds overlap substantially.  Or going in the other direction, if $K$ is low in the $K$-fold CV, the training sets would be quite different across folds, and the resulting models are more likely to be different (hence higher variance).  If the above argument is right, why would models learned with leave-one-out CV have higher variance? Can I set up WhatsApp on my desktop when my smartphone is broken? Can a wizard choose where to place their soul piece when creating a horcrux? How do I find the current machine's full hostname in C (hostname and domain information)? In a C project (POSIX), how do I get the fully qualified name for the current system?  For example, I can get just the hostname of my machine by doing gethostname() from unistd.h. This might give me machine3 in return, but I'm actually looking for machine3.somedomain.com for example.  How do I go about getting this information? I do not want to use a call to system() to do this, if possible. Notation: Why write the differential first? From reading answers here, I've noticed that some people write integrals as $\int dx \; f(x)$, while other people write them as $\int f(x)\;dx$.  I realize that there is no mathematical difference between the two notation forms, but was wondering why some people choose the first method over the second.  Is there some place in higher maths that it becomes beneficial to write the differential first?  (I, personally, have always used the second method, just because I was taught that way...) Is it possible to remove a user's password using the net command?  I tried "net user &lt;name&gt; *" and just hitting return twice, but this does not work as expected. Is there any other way to do this? (I'd gladly take non-net commands, as long as they are built-in in XP SP3).  Edit: Seems, I did not make my intention clear. I don't just want to change the password, but remove it completely (so that the user may log in without having to supply a password).  I'm familiar with the "net"-reference and have searched online for several hours, but could not find a hint on how to do this. Meta's tag pages inaccessible due to self-redirect loop Do Stack Exchange sites allow editing of comments and posts from other users? Recovering accidentally deleted files How do I rotate a tikz rectangle about a specific axis? I am trying to create a beamer animation using tikz, but I can't even get basic rotating of a tikz image working as desired.  I have a rectangle specified by  \draw[rounded corners,dotted] (-3.5,0) rectangle (-0.5,2);   I would like to rotate this rectangle about the point (-1,.5) (which is near the bottom right corner of the rectangle).  I've tried:  {\rotatebox[origin=c,x=-1,y=.5]{130}{             \draw[rounded corners,dotted] (-3.5,0) rectangle (-0.5,2);}}   But this produces an error.  If I just use the origin=c option, it compiles, but it rotates the rectangle about the point (0,0).  I've also tried it with just the x=-1,y=.5 (without the origin option), and it fails to compile.  I have searched the documentation, which is where I learned about the options x=xdim and y=ydim.  However, I can't find a single example demonstrating how these options should be used.  Any suggestions would be greatly appreciated.    Also, if there is a better command for rotating things that will be more suitable for use in a beamer animation, please let me know.  Thanks! So I was in the middle of making a ball-shaped smoke, but the volumetric effect didn't work following the basic shape. It remains cube in Eevee Blender 2.8; while in Cycle it works, but in Cycle it takes thousands of years for Render. How frequently can you ask for a personal reference without being disrespectful? What's the frequency of filesystem check on boot? What is the maximum number of times the root filesystem on this computer can be mounted before it is automatically checked? $$\frac{1}{z-\sin z}$$ $$\frac{1}{z(1-\frac{\sin z}{z})}$$  the laurent's transform is also used to simplify the function.  the residue is found a $\frac{2*36*2}{5}$ but the actual answer is given as $\frac{3}{10}$ the residue is given as The solution is incorrect and also the pole is of the order 3. Story about human space explorers who run into alien telepath space crew I read a short story in an anthology around 1998 (the book could have been older than that) which went like this - A human space exploration scientific crew is exploring an alient planet (peaceful planet, as I recall) when they run into an alien spaceship (from a different planet which also happened to be there) - the aliens were telepaths.   The alien commander and first officer discuss the earthlings after a meeting and realize that the human crew are the descendants of a species (Banthu/Klanthu/Zantha, something like that) which had tried to violently take over the galaxy some 20/30/50,000 years ago and which had been beaten back by the combined might of the rest of the galaxy. They had supposedly been eliminated but they somehow managed to survive and are back in space only a few thousand years after they were completely beaten (which is something the aliens are amazed by).   The alien commander kills the human explorers via telepathy but realizes that there is no information available to locate their home planet and speculate that they will be meeting again soon given the past history of the humans.  I vaguely think there was also a fantasy short by L Sprague de Camp in the same anthology, but can't be 100% sure. Any thoughts/ideas? Thanks! Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis Suppose that we do not know anything about the complex analysis (numbers). In this case, how to calculate the following integral in closed form? $$\int_0^\infty\frac{\cos x}{1+x^2}\,\mathrm{d}x$$ Payment from Apple for developer