A finite product of nilpotent groups is nilpotent
Why is the direct product of a finite number of nilpotent groups nilpotent?
Gauss law and electric flux Can you please explain me what is electric flux. I know it is $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$, but in many place its given flux means to flow. But how does electric field "flow"? Also if we assume its the electric field lines (can you also specify what exactly are these) are "flowing" how does $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$ give the total electric field lines passing through that area? (can you please elaborate when you explain?)  Pls. I know it shouldn't come here but there is no page for electric flux. Every finite commutative ring with no zero divisors contains a multiplicative identity? Calculate E[X] from incomplete data? The exercise I'm doing describes the random variable $X$ as the following  | Number of cars |  0  |  1 |  2 |  3 |  4+ |  | % of families  |  15 | 45 | 25 | 13 |  2  |   Then it asks me to evaluate $E[X]$. But if there could be cases with 4+ cars, wouldn't that make it impossible to calculate the expectancy? Calculating the limit $\lim((n!)^{1/n})$ Find $\lim_{n\to\infty} ((n!)^{1/n})$. The question seemed rather simple at first, and then I realized I was not sure how to properly deal with this at all. My attempt: take the logarithm,  $$\lim_{n\to\infty} \ln((n!)^{1/n}) =  \lim_{n\to\infty} (1/n)\ln(n!) =  \lim_{n\to\infty} (\ln(n!)/n)$$ Applying L'hopital's rule:  $$\lim_{n\to\infty} [n! (-\gamma + \sum(1/k))]/n! = \lim_{n\to\infty} (-\gamma + \sum(1/k))=  \lim_{n\to\infty} (-(\lim(\sum(1/k) - \ln(n)) + \sum(1/k))  = \lim_{n\to\infty} (\ln(n) + \sum(1/k)-\sum(1/k)  = \lim_{n\to\infty} (\ln(n))$$ I proceeded to expand the $\ln(n)$ out into Maclaurin form $$\lim_{n\to\infty} (n + (n^2/2)+...) = \infty$$ Since I $\ln$'ed in the beginning, I proceeded to e the infinity  $$= e^\infty  = \infty$$  So am I write in how I approached this or am I just not on the right track? I know it diverges, I was just wanted to try my best to explicitly show it. On the moderator , the tooltip will display the text used for voting on a question; this is incorrect.   Steps to reproduce:   Cast a vote for or against any candidate Undo that vote   At this point, the tooltip content is changed, at least for that candidate.  See screenshots:           As you can see, the message doesn't quite fit here; these are certainly not questions. Verify mysqldump backup is corruption free How do I enable the "Universe" repository? How do I get to the Universe Repository in supported versions of Ubuntu? How do you remove Subversion control for a folder? I have a folder, c:\websites\test, and it contains folders and files that were checked out from a repository that no longer exists. How do I get Subversion to stop tracking that folder and any of the subfolders and files?   I know I could simply delete the .svn folder, but there are a lot of sub-folders in many layers. Bash variable scope Please explain to me why the very last echo statement is blank? I expect that XCODE is incremented in the while loop to a value of 1:  #!/bin/bash OUTPUT="name1 ip ip status" # normally output of another command with multi line output  if [ -z "$OUTPUT" ] then         echo "Status WARN: No messages from SMcli"         exit $STATE_WARNING else         echo "$OUTPUT"|while read NAME IP1 IP2 STATUS         do                 if [ "$STATUS" != "Optimal" ]                 then                         echo "CRIT: $NAME - $STATUS"                         echo $((++XCODE))                 else                         echo "OK: $NAME - $STATUS"                 fi         done fi  echo $XCODE   I've tried using the following statement instead of the ++XCODE method  XCODE=`expr $XCODE + 1`   and it too won't print outside of the while statement. I think I'm missing something about variable scope here, but the ol' man page isn't showing it to me. Update 2014-04-17 04:47 UTC: Stable, with some odds and ends to clean up      The main MSO/MSE sites are stable, but there are plenty of corners left to sweep. For details, see:    Not all of them mind you, just Meta Stack Overflow into Meta Stack Exchange.  I'll have you know, factually, that we really did believe this would take place in six-to-eight weeks when it was , but we've finally got a tentative date established.  If things go according to plan, we'll begin the operation shortly after 8:30 PM EDT on the 16th, completing everything within a few hour window. Ideally, all service disrupting endeavors will be completed within the first hour, which include:   The availability of Meta Stack Overflow The availability of Stack Overflow (more on this shortly) The availability of Chat on Meta Stack Overflow   As you know, we'll be bolting on a standard issue per-site meta on Stack Overflow, while breaking the link between what will have become Meta Stack Exchange and Stack Overflow. There's some irritable innards in that particular region, so we'll be asking folks to expect the unexpected during the maintenance window. Affected sites will be in and out of read-only mode, or quite possibly just down for maintenance while we're doing the actual break.  I'll be posting a system message on both Meta Stack Overflow as well as Stack Overflow itself 24 hours before we begin the actual work.   Did I say tentative in a six-to-eight-something time frame again? Why yes, I did - we're currently running some tests on the dev tier to simulate the split as closely as possible, so that we can better anticipate quirks that we need to address prior to actually doing it.  Once the sites have actually been stood up functionally on the production tier, we're going to get to work on finishing touches. This will include things like site settings (which determine bits of text you see in the question prompts, rep thresholds, etc) and all sorts of other fine tuning.  Once we're done:   Stack Overflow will have a blank, empty child meta site just like every other site The new Meta Stack Exchange will be up and running All rooms on Chat Meta Stack Overflow will be moved to Chat Meta Stack Exchange  I'll send over about 150 - 200 questions from MSE to MSO, most of which will be tag or SO-specific feature related posts that got buried by the network stuff without resolution.   If the tentative date moves, I'll update this post with the new date. However, we do not anticipate this happening any later than Saturday, April 19 - in the case that we see down time we can't mitigate and need to do it on a weekend.  The ground work is basically done, we're finishing up sanity now with a great deal of confidence, and we're pretty certain that we'll hit between those dates, if not directly on the tentative 16th.  Questions? Kvetch? Anonymous confessions? Answer below, and I'll address each in comments. It is possible to press ⎇ Backspace on macOS in order to delete the previous word (left of the cursor), and ⌘ Backspace to delete the previous line (left of the cursor). If you have an external keyboard with a "delete" key (or the "forward delete key"), or are able to emulate the delete key via software, it is possible to press ⎇ Delete to delete the word to the right of the cursor. However, perhaps surprisingly, it is not possible to press ⌘ Delete in order to delete the line to the right of the cursor.  Now, I have only been able to make this possible by emulating a ⌘⇧→ and then a Backspace with BetterTouchTool. However, I want to avoid doing something like this because BTT does not work at a "low enough level" for me – that is to say, the action is not entirely reliable.  Is there any official macOS way to delete the line to the right of the cursor? QGIS Atlas generation for multiple map extents? I'd like to split strings like these  'foofo21' 'bar432' 'foobar12345'   into  ['foofo', '21'] ['bar', '432'] ['foobar', '12345']   Does somebody know an easy and simple way to do this in python? Does a linear operator obeying Leibniz rule imply it is a differential operator? What is the XY problem? What is the XY problem?  When asking questions, how do I recognize when I'm falling into it?  How do I avoid it? I remember reading a book in high school where a group of people travel to an alien planet where they discover an alien civilization separated into 2 castes. they are then made slaves to the taller class of aliens and one man has the flesh removed from his hands to make his fingers appear longer. std::string formatting like sprintf Is there a Linux equivalent of Windows' "resource files"? Super+D key shortcut does not show desktop I recently installed Saucy Salamander on my computer. Previously in Ringtail, Super+D used to show the desktop. However for this release, the Super+D does not seem to work properly... Is it a bug? Nikon d5100 producing extremely underexposed images