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"ERROR: Extra }, or forgotten \right." in align* enviroment Why do I get a "ERROR: Extra }, or forgotten \right." in the following align* environment?  \begin{align*}     \int\left[\left(\der{E_z}{y}-\der{E_y}{z}-\mu\der{\alpha}{t}\right)\alpha&amp;+\left(\der{E_x}{z}-\der{E_x}{x}-\mu\der{\beta}{t}\right)\beta\\     &amp;+\left(\der{E_y}{x}-\der{E_x}{y}-\mu\der{\gamma}{t}\right)\gamma\left.\vphantom{\left(\der{E_y}{x}}\right]d\omega=0.     \end{align*}   thanks Can a word be contracted twice (e.g. "I'ven't")? Taxonomy terms view sorting results numerically I have a taxonomy that's comprised entirely of numeric term names, 1 through 1200 (with a few numbers missing in between). I created a new "Taxonomy terms" view to show all terms in this vocabulary. When I look at the view results, I'd like to see the terms sorted numerically, however the view is displaying the terms alphabetically. I understand the reason for this is because term names are strings, but I'm hoping someone has an answer of how to make the query treat the term names as integers.  Here's an example of the view results as they are displayed now:   1 10 100 1000 1001 1005 101 1014 1015 1016 1019 102 1020 1024 103 1034 104   Normally in MySQL, you could write SELECT name FROM {taxonomy_term_data} ORDER BY CAST(name AS UNSIGNED). Is there a way to get this same type of CAST() happening in views? Why does copying the same amount of data take longer if spread across many separate files? I noticed that copying 24Mb worth of data from one folder to another took about 30 seconds because (I'm assuming this is the reason) it was over 1,000 separate files. Copying 24Mb shouldn't take so long. Why does the number of files make a different?  I'm running Windows 7 on a MacBook (4GB ram, Intel(R) Core(TM)2 Duo CPU P7450 @ 2.13GHz, 32-bit Operating System)  EDIT: NTFS is the file system used on the drive bash: alias: alias: not found Remotely run script on Unix, get output locally? I need to run a (Tcl, or whatever) script on a remote Unix machine, from a (local) Windows command shell, and I want the stdout/stderr of the script to show up in the Windows CLI. The exit code would also be useful.  Is this possible using ssh (putty)? Or by any other means?  Thanks! Compactness of $\operatorname{Spec}(A)$ In an exercise in Atiyah-Macdonald it asks to prove that the prime spectrum $\operatorname{Spec}(A)$ of a commutative ring $A$ as a topological space $X$ (with the Zariski Topology) is compact.   Now because the basic open sets $X_f = \{\mathfrak{p} \in \operatorname{Spec} (A) : \{f\} \not\subseteq \mathfrak{p} \}$ form a basis for the Zariski Topology it suffices to consider the case when   $$X = \bigcup_{i \in I} X_{f_i}$$   where $I$ is some index set. Then taking the complement on both sides we get that   $$\emptyset = \bigcap_{i \in I} X_{f_i}^c$$  so there is no prime ideal $\mathfrak{p}$ of $A$ such that all the $f_i$'s are in $\mathfrak{p}$. Now from here I am able to show that the ideal generated by the $f_i$'s is the whole ring as follows. Since there is no prime ideal $\mathfrak{p}$ such that all the $f_i \in \mathfrak{p}$, it is clear that there is no $\mathfrak{p}$ such that $(f_i) \subseteq \mathfrak{p}$ for all $i \in I.$ Taking a sum over all the $i$ then gives $$\sum_{i \in I} (f_i) = (1).$$  Now here's the problem:          How do I show from here that there is an equation of the form $1 = \sum_{i \in J} f_ig_i,$ where $g_i \in A$ and $J$ some finite subset of $I$?       This part has been giving me a headache. I am not sure if the finiteness bit has to do with algebra, topology or the fact that we are dealing with prime ideals.  This is not a homework problem but rather for self-study.  $\textbf{Edit:}$ I have posted my answer below after the discussion with Dylan and Pierre. How to input integer value to an array, based preceeding row + column values? Cardinality of $\mathbb{R}^\mathbb{R}$ by diagonal argument I want to prove that the set of all real functions $\mathbb{R}^\mathbb{R}$ has a higher cardinality than the real numbers $\mathbb R$, by Cantor's diagonal argument.  I'm having difficulties with approaching this problem.  What I'm looking for is a hint in the right direction.  I've seen an example where it is shown that the power set $2^S$ of a countable set $S$ is uncountable, by the diagonal argument. How precise is the frequency of the AC electricity network? If I make a digital clock which first detects the AC frequency roughly (whether it is 50, 60, 100Hz, etc), then uses it as its clock pulse source, how precise would it be? Would it work world wide precisely?  For instance, in USA, what is the mean and standard deviation of the 60Hz AC frequency? pass 1 environment variable using sudo Is this a correct way for passing an environment variable in sudo ?  sudo -u www-data -b env FOOBAR="foobar" /home/user/folder/daemon Is there a word that means "a span of six months"? That is, I want to connote a stretch of time that lasts half a year, not an event that happens every six months. ASP.NET Website's BIN directory and references Because the default 'Profile Graph' tool was not sufficient, I wrote a custom VBA script that creates scaled and exaggerated profile cross-sections in ArcGIS but I need more features:   Visualize more than 1 surface Visualize vertical and directional boreholes Ability to symbolize / edit the output Linked with underlying data - changes in terrain (or profile 3D line) reflected in output   A few years ago I tested an extension by A-Prime software called 'CrossView For ArcGIS' but I am not sure if it is compatible with ArcGIS 10 (Contacted A-Prime but they have not yet responded)   Area there any alternatives? Other 3rd party software? A functioning script? that can do this? How to automate generation of image files? This is the profile of the object I'd like to wrap...    Here is the object's profile after being wrapped...    Is it possible to prevent the distortion? The following post here:  did not affect my object. It seemed very promising, maybe I'm missing something?  Note: I have applied the scale to both my object and curve. How to attach my repo to heroku app Determine whether the series $\sum_{n=1}^{\infty}(\frac{n}{n+1})^{n^2}$ is convergent or divergent.  I've tried applying all the basic tests to no avail. I need to find out what the "trick" for this particular series is. apt-get build-dep is unable to find a source package I have already followed  to disable middle mouse button paste on my Ubuntu 12.04.   Works like a charm.   Now I am trying to achieve the same on my Linux Mint 17. When I try to  sudo apt-get build-dep libgtk2.0-0   it gives me the following output:   Reading package lists... Done Building dependency tree        Reading state information... Done Picking 'gtk+2.0' as source package instead of 'libgtk2.0-0' E: Unable to find a source package for gtk+2.0   For me it looks like apt-get is somehow "resolving" 'libgtk2.0-0' to 'gtk+2.0', but then does not find any package named like that.   EDIT:  although I am now able to compile the program (see my answer), I still do not know what  Picking 'gtk+2.0' as source package instead of 'libgtk2.0-0' is supposed to mean. Any insight on this would be appreciated, thanks! What is the difference between test set and validation set?