A user on Chemistry SE mentioned a very nice shortcut to use in implementing a command for partial derivatives (see comments section of question: ):  Suppose you want to create the following partial derivative:  \left(\frac{\partial U}{\partial p}\right)_{\!T}   using this command:  \newcommand{\pd}[3]{\left(\frac{\partial #1}{\partial #2}\right)_{\!#3}}   The standard use of the command would be:  \pd {U}{p}{T}   However, since each argument is only a single character, this is sufficient:  \pd UpT   If one needs to typeset numerous partial derivatives, this is a great time-saver.    Indeed, you can even use a hybrid approach, where braces are eschewed for single-character arguments, but used for multi-character arguments.  For example, to implement this:  \left(\frac{\partial U}{\partial p}\right)_{\!T, n_i}   One would write this:  \pd Up{T, n_i}   This seems to leverage what is a standard shortcut in LaTeX for single-argument commands (e.g., we drop the braces when the argument of a superscript or subscript command has only one character). But, for this usage (multi-argument user-defined commands) are there cases in which this (seemingly non-standard) approach would create a problem?
Sometimes writing braces and omitting them produces the same result:  \tilde{\psi}  \mathrm{e}^{\mathrm{i} \pi}   vs  \tilde \psi   \mathrm e^{\mathrm i \pi}   Or (taken from Werner's comment below)   \frac{1}{2} vs \frac12   If that's the case, how bad for the quality of my code is omitting them? Of course, if one compiles a pair of formulas, there is no difference. But, since I ignore how TeX works, my point is: if one writes long codes with these habits,   doesn't TeX go somehow crazy because I'm not writing as it expects?   For instance, does it have any effect on how fast are long documents compiled? Any reason to keep them?
To infinitive used after adjective This question is relatively simple. I don't understand why we never use passive form of to infinitive after the adjective unless the subject is "it".  For example:     He is difficult to please.   People consider the example above a correct sentence. But:     He is difficult to be pleased.    People, for example, my teacher, said it sounds wrong and told me not to write this type of sentence. Is it grammatically flawed, or is it just a stylistic choice? How to close aberrant tooltips in Windows So, here I am, trying to watch The Cleveland Show (TM).      And, as happens from time to time, some program or another has left a modal tooltip.  I don't know which program; how can I lose the tooltip, short of logoff/reboot?  Currently happening on Windows 10, but I have seen it on other versions. Calculate $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ After I just learned there are ways to cancel out $0$s in the divisor of fractions onto limits I looked back at a task where I gave up when I got the result $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ so I tried to find a way to get the $0$ out here, as well. Am I just not seeing the solution or is there no way to do it? Why Are Ethernet/RJ45 Sockets Magnetically Coupled? As the title says really, why do ethernet sockets need to be mag-coupled? I have a basic understanding of electronics, but mostly, I can't figure out the right search terms to google this properly. Unable to cover get set in apex test class Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are curved into the 4. dimension so that they can travel without acceleration in straight opposite directions and yet meet each other time after time.  On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to , so that one frame is preferred - but which one?  So the question is: Who will be older? And why?  And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower...  How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT?  And if we are back to a situation with a preferred frame: what is the difference to the classical Galilean transform? Don't we get all the problems back that seemed to be solved by RT - e.g. the speed limit of light, because if there was a preferred frame you should be allowed to classically add velocities and therefore also get speeds bigger than c ?!? (I know  is only a local theory but I don't understand why the global preferred frame should not 'override' the local one).  Could anyone please enlighten me (please in a not too technical way because otherwise I wouldn't understand!)  EDIT Because there are still things that are unclear to me I posted a follow-up question: Let R be a commutative ring with an identity such that for all $r\in$ R, there exists some $n&gt;1$ such that $r^n = r$. Show that any prime ideal is  maximal. (Atiyah and MacDonald, Introduction to Commutative Algebra, Chapter 1, Exercise 7.)    Any hints? Count the number of fish caught in total if we are given the number of fishermen who caught at least $n$ fish. Some fishermen caught some fish. No one caught more than 20 fish. $a_i$ is the number of fishermen who caught at least $i$ fish. How many fish were caught?   So my guess is that the number of fish caught has to be $$ a_1+a_2+\ldots + a_{20}$$  I reason that if a fisher man caught $n$ fish then he will appear in the tally $n$ times.   Is this logic correct? I was surfing the internet the other day when I found this phrase: Instead your precious time and attention is wasted. To my ears, it sounds wrong. But I'm not a native English speaker, so I consulted with a number of them, and some of them said that it was "is" because the adjective modifies only the noun "time" and not "attention". Others said it "is" because that's just how it is. But I still believe it should be "are". Any help is appreciated. Set multicolumn width to default table width How do CSS triangles work? How should I add users non-interactively? I have a set of users I need to add to a new system as part of a BASH script that preps my server. How can I non-interactively add the user, create their home directory, set the group, and enter a default password?  For example, if I needed to add the following users, how would I go about that?  user: node password: spoon group: ultraMegaPermissions  user:serve password: spoot group: sortaNotMega  user:watcher password: spoogle group: notMega I'm rotating an object on two axes, so why does it keep twisting around the third axis? I see questions come up quite often that have this underlying issue, but they're all caught up in the particulars of a given feature or tool. Here's an attempt to create a canonical answer we can refer users to when this comes up - with lots of animated examples! :)    Let's say we're making a first-person camera. The basic idea is it should yaw to look left &amp; right, and pitch to look up &amp; down. So we write a bit of code like this (using Unity as an example):  void Update() {     float speed = lookSpeed * Time.deltaTime;      // Yaw around the y axis using the player's horizontal input.             transform.Rotate(0f, Input.GetAxis("Horizontal") * speed, 0f);      // Pitch around the x axis using the player's vertical input.     transform.Rotate(-Input.GetAxis("Vertical") * speed,  0f, 0f); }   or maybe  // Construct a quaternion or a matrix representing incremental camera rotation. Quaternion rotation = Quaternion.Euler(                         -Input.GetAxis("Vertical") * speed,                          Input.GetAxis("Horizontal") * speed,                          0);  // Fold this change into the camera's current rotation. transform.rotation *= rotation;   And it mostly works, but over time the view starts to get crooked. The camera seems to be turning on its roll axis (z) even though we only told it to rotate on the x and y!    This can also happen if we're trying to manipulate an object in front of the camera - say it's a globe we want to turn to look around:    The same problem - after a while the North pole starts to wander away to the left or right. We're giving input on two axes but we're getting this confusing rotation on a third. And it happens whether we apply all our rotations around the object's local axes or the world's global axes.  In many engines you'll also see this in the inspector - rotate the object in the world, and suddenly numbers change on an axis we didn't even touch!    So, is this an engine bug? How do we tell the program we don't want it adding extra rotation?  Does it have something to do with Euler angles? Should I use Quaternions or Rotation Matrices or Basis Vectors instead? Find all natural numbers $n &gt; 1$ and $m &gt; 1$ such that $1!3!5!\cdots(2n - 1)! = m!$   I have been thinking about coming up with some inequalities which would narrow the possible range of pairs $(n, m)$, however the best I have been able to find so far are $m \ge 2n - 1$ and $m \lt n^2$, which is clearly not enough.  Update. The question has tag combinatorics as it is from a book about combinatorics, so there must be at least partly combinatorial solution. $24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement. What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.  What are good introductory guides to QM along these lines? How can I write % into a file? How can I write % into an auxiliary file? % will not work, because LaTeX thinks that I start a comment with it (in the main file, not in the auxiliary file!), and \% will write \% into the file. How can it be accomplished?   \documentclass{article} \begin{document} \newwrite\outfile \immediate\openout\outfile=example.dat \immediate\write\outfile{%}% will not work, of course, but neither \% \immediate\closeout\outfile \end{document} What are examples where a "naive bootstrap" fails? What is the official name for the "special" ASP.NET tags like this:  &lt;%# %&gt; &lt;%= %&gt; &lt;%@ %&gt; &lt;%$ %&gt;   I can't seem to figure out the conceptual or well known name for these, so I'm having trouble searching for more info.  As a bonus, can anyone give me a quick rundown of all of the possible "special tags" and what each one of them does (or point me to a resource)? default constructor for int