Solving $2x^4+x^3-11x^2+x+2 = 0$
Equation with high exponents
A topological space is extremally disconnected iff every two disjoint open sets have disjoint closures Show that for any topological space $X$ the following are equivalent:         $X$ is extremally disconnected   Every two disjoint open sets in $X$ have disjoint closures.      My attempt at a solution  Assume every two disjoint open sets in $X$ have disjoint closures. Let A open in $X$, $A$ and $X \setminus \overline{A} $  disjoint open set $\overline{A} \cap (\overline{X \setminus \overline{A}} )= \emptyset$,  $(\overline{X \setminus \overline{A}} ) \subset X \setminus \overline{A}$, which implies that $X \setminus \overline{A}$ is closed in $X$. Thus $\overline{A}$ is open in $X$. So we obtain $X$ is extremally disconnected.  Otherwise Let $X$ is extremally disconnected. Then the closure of every open set is open.  So $X$ is completely separated. Let $A$, $B$ two disjoint open sets.  Then there exist a continuous function $g:X \rightarrow [0,1]$ such that  $g(A)=0$, $g(B)=1$  How can I continue? I am trying to put in a switch and a light it controls in a storage building and  is how I wired it.   Click for larger view  When I checked the wiring it registered 120V when the switch was on, and right around 50V when the switch was off.  Why would power still be getting to the light (I'm guessing there is a problem with the switch) and why would it only be 50V?  Oh, and where everything branches off at the beginning I have a junction box there where all of the wires are joined there. It is a common assumption (and, as far as historical stock market data goes, also proven) that the stock market is always growing if you enlarge the time window long enough . In other words: The stock market always goes up in the long term. Is, therefore, the conclusion valid that you can totally invest as much as you want at any point in time you want and you can never go wrong, if  You diversify strong enough (invest &quot;in the world&quot;) You do not need to urgently sell your assets at any point in time  If yes, all that strategies that rely also on diversified, long-term investments (Dollar-Cost-Averaging &amp; Rebalancing, .. what others do you know?) are just to optimize the yiels, but you'd make profit even without those strategies. Is that correct? I am looking for a word that would describe being obsessed with the details of a larger entity such that the "looker" neglects to see the whole or (perhaps more importantly) the purpose of the whole.  Basically, "not seeing the big picture".  What can [more] succinctly describe this?  Edit: I just found this post: . I think I want the exact opposite. Passing Account ID to my Visualforce Page As the user goes into an account, there is a custom button that they can click that will redirect them to my Visualforce page.  How can I capture that account id  in my controller?  Thanks  public myControllerCBR(){     breachRecord = new List&lt;wrapperClass&gt;();      AccountTeamMember uId = [SELECT UserId FROM AccountTeamMember WHERE AccountId =:ApexPages.CurrentPage().GetParameters().Get('id') and TeamMemberRole = 'Sales Engineer' limit 1];      List&lt;User&gt; uName = [SELECT Name, Manager__c, MANAGERID, Email, MOBILEPHONE FROM User WHERE Id =:uId.UserId limit 1];       for(User rept : uName){         breachRecord.add(new wrapperClass(rept));     }  }   See button setup: Persistent Dummy Output The soundcard I want to use is detected and works (it only recently switched to dummy output and didn't allow me to go back). HDMI is no longer listed under Audio and Video - KDE Control Module; everything under audio module is set to dummy output and its the only 'soundcard' on the list now. I can view my previous sound cards in alsamixer, but changing the settings from there does nothing. How can I get my real soundcards to work again? I have already tried the following answers without success:  EDIT: name@name-desktop:~$ lspci -vvv | grep -A8 Audio 00:01.1 Audio device: Advanced Micro Devices, Inc. [AMD/ATI] Kaveri HDMI/DP Audio Controller         Subsystem: ASRock Incorporation Kaveri HDMI/DP Audio Controller         Control: I/O+ Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx+         Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=fast &gt;TAbort- &lt;TAbort- &lt;MAbort- &gt;SERR- &lt;PERR- INTx-         Latency: 0, Cache Line Size: 64 bytes         Interrupt: pin B routed to IRQ 43         Region 0: Memory at ff764000 (64-bit, non-prefetchable) [size=16K]         Capabilities: &lt;access denied&gt;         Kernel driver in use: snd_hda_intel         Kernel modules: snd_hda_intel -- 00:14.2 Audio device: Advanced Micro Devices, Inc. [AMD] FCH Azalia Controller (rev 01)         Subsystem: ASRock Incorporation FCH Azalia Controller         Control: I/O- Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-         Status: Cap+ 66MHz- UDF- FastB2B- ParErr- DEVSEL=slow &gt;TAbort- &lt;TAbort- &lt;MAbort- &gt;SERR- &lt;PERR- INTx-         Latency: 32, Cache Line Size: 64 bytes         Interrupt: pin A routed to IRQ 16         Region 0: Memory at ff760000 (64-bit, non-prefetchable) [size=16K]         Capabilities: &lt;access denied&gt;         Kernel driver in use: snd_hda_intel  Could this image possibly help?:  There is another soundcard but I'm unsure of what its for because it never outputs sound, but it does have a lot of settings: that sound card is labelled as &quot;HD-Audio Generic&quot;.   So I went into Software &amp; Updates under the Additional drivers tab and I see this:  It was on Do not use the device so I changed it and applied the settings but unfortunately the soundcard isn't back even after reboot. The scenario:  In a bash script, I have to check if a password given by a user is a valid user password.   I.e suppose I have a user A with password PA.. In the script I asked user A to enter his password, So how to check if the string entered is really his password?... How do I unset an element in an array in javascript? Sort order in Windows Explorer The behaviour described below occurs on Windows-7 systems and on Windows XP. We operate in a dual-language environment - English and Hebrew.  When in Windows Explorer we sort files by name, the order in which they are listed is not what we would expect. Here is a list of file names as sorted by Windows Explorer (all of the files have a .pdf suffix):   1G110033H-PP 19C050G-PP-ORB 19C050H-PPRM 19C100H-PPRM 19C-MBPS-PP 19C-MBPS-PP-1 29AAC050-PP 29AAC100-PP 29AAC100-PPUL   29B004064-PP 101AC050-PP 101AC100-PP 101B100-PPE 1091003G-PPFSUL 10108033G-PPSA 10125033H-PPM     It looks to me that first the items are sorted according to the position of the first alphabetic character in the name, and then, within those groups, they are sorted in "normal" alpha-numeric order.  That is, all the files with an alpha character in the first position are on top of the list, followed by those with the first alpha character in the second position, followed by those with the first alpha character in the third position, and so on.  An alternate way of looking at this is that, in a file name composed of numbers and letters, the sort treats the first group of numbers in the name as the major sort node, with the rest of the name being the secondary sort node.  Now that I understand the sequencing logic, it's not a big problem, but I was wondering why this happens? I want to save a backup of my data on a remote server, but never want the backup server to see the data unencrypted. Editing a single file and backing up should not result in everything being encrypted and sent again. The remote server should preferably not even know the directory structure (and especially not the directory names).  Is there such a solution? Now that  is in effect, people who have visited Iraq, Syria, Iran, or Sudan since 2011 are banned from entering the US under the Visa Waiver Program. However it's unclear to me how could the US officials prove one has set foot in those countries, unless:   There's a stamp in one's passport indicating so, which can be side-stepped by getting a fresh passport One mentions the fact on the ESTA application form, which is obviously easy to avoid   Is there any other way the US might be able to identify such individuals?  NB: I'm not eligible for the VWP myself and don't plan to travel to the four countries above, so it's a purely theorethical question Will Find my iPhone Lost Mode be useful if stolen phone as shows Offline? My phone was stolen last night. I made sure it was in Lost Mode in iCloud and it was immediately in Offline status when I open iCloud. I am positive the thief switched it off. Now I am 100% certain the Find my iPhone option was turned on on my iPhone, but will the "Lost Mode" be of any help if it was not turned on on the iPhone? Would it be showing "Offline" if I did not turn on the option? How to determine the amount of experience needed for leveling up Related questions under this topic might include:   How should I base how much experience points it takes to get to the next level? What factors are involved in this? How do I keep the player not entertained long enough till he levels up? How can I vary the way the player gets experience points? I always see commands like this  apt-get -y install    What is the -y tag for and what is the difference between apt-get install with and without the -y tag? I am using extensively trigonometric functions when an angle is given in degrees. Some of these functions like sine or cosine have rational values, for example, the well   known example is that $\cos(\theta) =0.6 $ and $\sin(\theta) =0.8 $.       However besides the case of multiplicity of $90^\circ$ it seems there are no rational numbers $\theta$  with simultaneously rational  values of  sine and cosine.      Is it possible somehow to prove that for rational values of an angle given in degrees there are  no values simultaneously rational of sine and cosine functions, beside obvious case of multiplicities of $90^\circ$? What is an "AppImage"? How do I install it? I just read . It talks about downloading an AppImage.     Yes, Linux; the Linux packages is distributed as an .appimage for 32-bit and 64-bit distributions, and should run across all major Linux distributions without any issues. The team currently have no plan to provide a native .deb (or .rpm) installer.   What are AppImages? How do they differ from snaps? I masked an image in the UV/Image editor masking section. I then used that mask in the compositor for background replacement. However, the mask size seems to be different. Why is that? Here's a screenshot: NetworkOnMainThreadException on higher API Installing gcc-7 (and newer packages) in Ubuntu 16.04 When I gain control of a creature, do I also gain control of any auras or equipment attached to it? What would happen if I 'd a creature that had been enchanted by a bestow creature and cast a spell to give it protection from the enchantment's color on it to remove the bestowed creature?  For instance:  They have just bestowed a  on a  and passes the turn. I use Portent of Betrayal to take control of the Asphodel Wanderer, attack and in the second main I cast Gods Willing to give the Asphodel Wanderer protection from black. Nighthowler detaches and where does it go, my control, opponents control or graveyard?  As an additional question, in the same vein:  What if I destroyed the creature while it was on my side? So change the gods willing to a hero's downfall in the example.  Relevent (under state-based actions):     704.5n If an Aura is attached to an illegal object or player, or is not attached to an object or player, that Aura is put into its owner's graveyard.