Under what specific cases does searching for a number redirect to the question with that ID?
Inconsistent behavior when typing a number into the search field
How many physical degrees of freedom does the $\mathrm{SU(N)}$ Yang-Mills theory have? This is an exercise from my calculus class. The function is defined as $x\sin (1/y)+y\sin (1/x)$ if $x\neq0 $ and $y\neq0 $, and $0$ if $x=0 $ or $y=0$.  I'm pretty confident the limit exists and should be $0$, because: $$\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]=\lim_{(x,y)\to(0,0)}[x\sin (1/y)]+\lim_{(x,y)\to(0,0)}[y\sin (1/x)]$$  And: $x\leq x\sin(1/y)\leq x$, so $\lim_{(x,y)\to(0,0)}[x\sin (1/y)]=0$ right? (The same can be said for $\lim_{(x,y)\to(0,0)}[y\sin (1/x)]$)  However, I tried checking my answer, and according to Wolfram Alpha the limit doesn't exist. Is this because I'm wrong, or is it just because $x\sin (1/y)+y\sin (1/x)$ is undefined for $y\neq0 $ and $y\neq0 $ Was Elrond, in Tolkien's opinion, more inherently powerful than Galadriel? I always thought it was the other way around, but then I read this (Letter 246):     "Of the others only Gandalf might be expected to master him – being an emissary of the Powers and a creature of the same order, an immortal spirit taking a visible physical form. In the 'Mirror of Galadriel', 1381, it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power."   This "especially Elrond" confuses me. I don´t think that Elrond is inherently more powerful than Galadriel, who is described as the greatest of the Noldor, except for Fëanor (and possibly even his equal).  A quote from Unfinished Tales says:     "...In this he (Tolkien) emphasized the commanding stature of   Galadriel already in Valinor, the equal if unlike endowments of   Fëanor; and it is said here that so far from joining in Fëanor's   revolt she was in every way opposed to him."   Furthermore,      "A queen she was of the woodland Elves, the wife of Celeborn of   Doriath, yet she herself was of the Noldor and remember the Day before   days in Valinor, and she was the mightiest and fairest (so even   fairer than Arwen I would guess) of all the Elves that remained in   Middle-earth."   (The Silmarillion, of the Rings of Power)  And again...     "Galadriel was the greatest of the Noldor, except Fëanor maybe, though   she was wiser than he, and her wisdom increased with the long years."   (the Shibboleth of Fëanor)  Restating it:     "These two kinsfolk (Fëanor and Galadriel), the greatest of the   Eldar in Valinor, were unfriends for ever." "Who together with the   greatest of all the Eldar, Luthien Tinuviel, daughter of Elu Thingol,   are the chief matter of the legends and histories of the Elves."   (Unfinished Tales)  The latter means that Luthien, Fëanor and Galadriel are the chief matter of the history and legends. It seems to me that Tolkien thought of those three as the creme de la creme of the elven crop.  Reading all that I have serious problems believing that Elrond could be superior to her. As great as Elrond is, descending from Melian, he is no equal of Fëanor, who is said to be the mightiest of all elves, and if Galadriel is his equal, then there is no way that Elrond would be mightier than her.  Maybe I just read this "especially Elrond" wrong; it could as well mean that especially Elrond was deceived into thinking that he could master the ring, because that was the deceit of the ring. And Tolkien said explicitly that only Gandalf could possibly master it.  So, what do you think? I have a small question regarding using sudo with output redirect &gt;. To enable IP forwrding, someone can use the command:  echo 1 &gt; /proc/sys/net/ipv4/ip_forward   Executing this command will give permission denied as it requires root privileges. However, executing the same command with sudo gives also permission denied error! It seems that output redirect &gt; does not inherit the permissions of the preceding command echo. Is this right?  As a workaround I do:  echo 1 | sudo tee /proc/sys/net/ipv4/ip_forward   Is this the best way to do it? Am I missing something?  Please, note that this is an example and it applies to all commands that use output redirect. For $G$ group and $H$ subgroup of finite index, prove that $N \subset H$ normal subgroup of $G$ of finite index exists The website I'm working is allegedly going to have a massive hit rate soon after launch. The client is talking about the possibility  of around 2500 hits per second over a day or so.   Ignoring the fact that this hit rate is probably wild client optimism and apart from getting the largest servers possible, what is the best way that Drupal should be configured to support a large hit rate.  I've read Scaling the , ,  and many other pages, but what I'm looking for is real experience of doing this, what works, what doesn't, and what to expect. What do people who are using a pensieve look like? As far as I remember from the books, there's no description of what a person using a Pensieve looks like. When Harry is using the Pensieve, he describes it as if he were falling into it, but it's never stated whether his body really enters the Pensieve, because the experience is just told from his point of view.   Now let's say Dumbledore enters his office while Harry was using the Pensieve -- what would Dumbledore see? Is there an answer in the books/canon? What is the difference between these two ways to calculate average velocity? Average velocity:  $$v_{\rm avg,1}=\frac{v_{\rm final}+v_{\rm initial}}{2}$$   and average velocity:   $$v_{\rm avg,2} =\frac{\rm total\;displacement}{\rm time \;taken}=\frac{\Delta x}{\Delta t} $$  What is the difference between them and when do we use them? 16.04 Upgrade: Failed to fetch Empty files can't be valid archives Is there a saying or idiom for "trying to get the truth from someone by lying"? context   Mary-Ann got home late from school.  Asked where she had been, she said she had spent the afternoon at the library.  Her father thinks she is lying and says: "I know you haven’t been there because I was there myself".  He is lying because he thinks she will tell the truth if she realizes she has been caught. boyfriend – “your sister told me everything” (sister did nothing) -  girlfriend – “Oh, did she? I’m gonna kill her.    The rationale for doing this is to catch someone by surprise so he will admit having lied.  Soemtimes, however, the person isn’t lying and the real liar will have to reap the consequences of his reproachable action, having to admit he was just/it was just ...........(saying or idiom)..... How to send mail from the command line? How to send mail from the command line? Do I need a bus/train/plane ticket out of Thailand in order to get a Visa-on-Arrival? Someone told me I need a ticket out of Thailand in order to enter.  I am traveling to Thailand, on March 18th. I have a Ticket from Bangkok to Sweden booked for June 4th.   I will be staying in Thailand for 2 weeks when I arrive there, then traveling around Cambodia, Laos and Vietnam until June 4th when I leave.   With that ticket out of Thailand, will I be able to get in and get a (30 day) Visa-On-Arrival (or not because the ticket out is not within the first 30 days). Or do I need to show proof that I am leaving within 2 weeks of being there at first? I wanted to switch to Xfce (I had KDE and GNOME installed), and I did this :    sudo apt-get install xubuntu-desktop sudo apt-get remove kubuntu-desktop sudo apt-get remove ubuntu-desktop sudo apt-get autoremove   but to my surprise, I could still pick gnome, kde plasma, etc during the log in.  So, how do I completely remove KDE and GNOME desktops? How can I capture KeyDown event on a WPF Page or UserControl object? I have a Page with a UserControl on it.  If the user presses Esc while anywhere on Page I want to handle.  I thought this would be as easy as hooking up the PreviewKeyDown event, testing for the Esc key, and then handling it.  However, when I placed I breakpoint in the event handler I found it was never getting called.  I thought perhaps the UserControl might be getting hit, so I tried PreviewKeyDown there... same result.  Does anyone know the proper place to test for a KeyDown or PreviewKeyDown on a Page object? How do you disable autocomplete in the major browsers for a specific input (or form field)? Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$ I need to show that  $$ \int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3} $$  I have already derived the result $\int_0^\infty \frac{\sin^2x}{x^2} = \frac{\pi}{2}$ using complex analysis, a result which I am supposed to start from.  Using a change of variable $ x \mapsto 2x $ :  $$ \int_0^\infty \frac{\sin^2(2x)}{x^2}dx = \pi $$  Now using the identity $\sin^2(2x) = 4\sin^2x - 4\sin^4x $, we obtain  $$ \int_0^\infty \frac{\sin^2x - \sin^4x}{x^2}dx = \frac{\pi}{4} $$ $$ \frac{\pi}{2} - \int_0^\infty \frac{\sin^4x}{x^2}dx = \frac{\pi}{4} $$ $$ \int_0^\infty \frac{\sin^4x}{x^2}dx = \frac{\pi}{4} $$  But I am now at a loss as to how to make $x^4$ appear at the denominator.  Any ideas appreciated.  Important: I must start from $ \int_0^\infty \frac{\sin^2x}{x^2}dx $, and use the change of variable and identity mentioned above Ideally, I'd like to write a unit test to help me "dummy check" for unexpected effects of the upcoming guest user sharing setting changes.  We'd had some controller/trigger code "gracefully handling" data it couldn't see thanks to the new sharing restrictions ... which resulted in simply "not doing" some work that it was supposed to do, which from a business process perspective isn't "graceful" at all (it was an important automation for downstream processes).  I'd like to write up a unit test with some system.assert statements validating that "data still goes where it's supposed to" when the "submit" button a public-facing Visualforce page of a community is clicked.  Unfortunately, I can't seem to make the "submit" button on a Controller for a public-facing Visualforce page work in the context of a unit test because the record whose creation it results in doesn't get its corresponding "sharing setting" record created in time for the execution context to pick it up.  I did a little proof of concept here ...  @isTest public class TestClass {      private static Id guestProfileId = Util.getProfileIdByName('Public Facing Portal Profile');     private static User guestUser;     private static Id portalGroupId = [SELECT Id FROM Group WHERE Name = 'Public_Portal' LIMIT 1][0].Id;      private static Custom_Object__c co;       private static testMethod void runTest() {         createCO();         Test.startTest();         // Note that putting createCO() inside the test and doesGuestSharingRuleExistForCO() doesn't help.         // That's what I was afraid of.         try {             doesGuestSharingRuleExistForCO(co.Id);         }         catch (Util.DeveloperException e) {             System.assert(FALSE, e.getMessage());         }         Test.stopTest();     }       private static void cacheUsers() {         guestUser = [SELECT Id FROM User WHERE profileid = :guestProfileId AND IsActive = TRUE LIMIT 1][0];     }      private static void createCO() {         co = new Custom_Object__c();         INSERT co;     }      private static void doesGuestSharingRuleExistForCO(Id coId) {         List&lt;SObject&gt; existingSharingRulesOnCO = [             SELECT Id FROM Custom_Object__share             WHERE RowCause = 'GuestRule' AND AccessLevel = 'Read' AND ParentId = :coId AND UserOrGroupId = :portalGroupId LIMIT 1         ];         if ( existingSharingRulesOnCO.isEmpty() ) { throw new Util.DeveloperException('Guest User sharing is not on for this custom object ID'); }     }      private static Boolean isCOSharingFlippedOnAtAll(){         String lookingFor = 'Custom_Object__Share';         for (Schema.SObjectType sObjectType : Schema.getGlobalDescribe().values() ) {             String sobjName = String.valueOf(sObjectType);             if (sobjName.contains(lookingFor) ) { return TRUE; }         }         return FALSE;     }  }   Am I just out of luck?  Is there no way to properly unit-test the effects (to automations relying upon "guest user" sharing settings when running as "guest user") of simulating the insertion of records into my database from a Visualforce page, due to not being able to separate out "execution context" enough and "wait" for the sharing rule record for the new record to come into existence? How can I use Photoshop to imitate a photo taken with a low-quality camera? How can I create an image in Photoshop that imitates a photo taken with a low-quality phone camera? Examples of qualities I want to simulate:   blurring in some areas caused by a dirty lens low quality exposure handling in the darkroom noise   Some examples: When I use \listoftables and \listoffigures I get in the list long captions that appear next to the tables/figures.  I would like to use short captions for this list which summarize these captions. Is that common to do? If so, what is one way to do it? Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .