How does one prove the following using natural deduction: $a ∧ ¬a \vdash b ∧ ¬b$
Formal proof for $q \land \neg q \vdash r \land \neg r$
Some people (me) would prefer the straight GNOME experience as opposed to the Unity style desktop offered in Ubuntu 17.10.  How can I get the standard GNOME desktop and interface? I have a bunch of external and internal HDDs that I use on a Linux system. I only have Linux systems, so using a Linux file-system would only make sense, right? However I'm currently using NTFS everywhere, because it gives me the most usable space out of HDDs.  I would like to switch to Linux file-systems now though, mostly because of permissions and compability (e.g. I can't get my LUKS encrypted NTFS partition to resize under Linux, keeps telling me to chkdsk under Windows).  However when I formatted those HDDs I tried out a bunch of different filesystems and every Linux filesystem, even ext2 which as far as I know has no journaling, used a lot of space for itself. I don't recall exact values, but it was over 100GB that NTFS got me more on a 2TB HDD, which is a lot.  So my question is: Is there a way to make ext-filesystems use less space for themselves? Or is there another filesystem (I've tried ext2, ext3, ext4, NTFS and vfat - None of them came even close to the usable space NTFS offered me) with perfect Linux support and great usable space?  I'd love to hear about how and why filesystems (especially ext2 which has no journaling) use that much more space than NTFS and I don't know where else to ask. I'd mostly prefer a way to use ext4 without journaling and anything else that uses up this much space, if that's possible. If parsing the output of ls is dangerous because it can break on some funky characters (spaces, \n, ... ), what's the best way to know the number of files in a directory?  I usualy rely on find to avoid this parsing, but similarly, find mydir | wc -l will break for the same reasons.  I'm working on Solaris right now, but I'm looking for a answer as portable across different unices and different shells as possible. Option to be notified when a post I downvoted is edited Prologue:  This is an effort to follow up on  which is marked as a duplicate of  highly voted and status-declined feature request (although they seem to be different, one focusing on the OP and the other on the downvoter).   My New Year's resolution was to downvote more.  So on January 3rd or so, I saw a post that was low quality, and downvoted.  Two days later, I came back to see if it was ready to be deleted or had gotten piled with downvotes, to find it with a significant positive score!  At which point, I noticed that the answer had been significantly improved.  So I retracted my downvote, changed it to an upvote, and immediately resumed my dearth of downvoting again.  I think I have a responsibility to downvote bad posts, despite that oh-so-painful -1 rep penalty.  But if I am also going to have the responsibility to follow up on every downvote I cast, I'm not going to bother. I don't want my downvote to leave a residual penalty on posts that were once low quality, and I am not going to trouble myself to keep checking up on every post I downvoted.  Can a downvoter have an option to be notified when a post they voted down was edited?  I wouldn't make this an automatic thing, because not all downvoters want it, and it isn't applicable to all cases of downvoting (although  that this should be part of the responsibility of a downvoter).  Personally, I would make this a universal toggle on-off option on the user profile page, not a question-by-question option, but I don't have strong feelings about it. Why does time change in Ubuntu after installing Windows Today I was installing Windows 7 on the same computer I have Ubuntu. For some reason, after installing Windows 7 and going back to Ubuntu the time went from the correct hour at that moment, 12:30PM to 7:30AM. This happened after installing Windows 7. For what I understand the BIOS has a time set, Ubuntu has the same time that is shown in the BIOS when installing it. At least up to this point is what I have seen. Now after installing Windows 7 (And believe me this is only for testing the performance of Windows 7 against Ubuntu in which case Windows 7 is falling behind a lot on the same hardware) the time changes in Ubuntu to the wrong one that is set in Windows 7.  I actually do not change the time in Windows 7 since this is one of the checks I am doing to see if the operating system can correctly grab the time. Windows 7 fails. Ubuntu does not BUT Windows 7 actually changes the time for Ubuntu if I boot with it afterwards.  So my question is, why/how does time change in Ubuntu after installing Windows.  NOTE - I have set Ubuntu time to "manual" instead of grabbing it from the Internet just to test out this. Can't install Oracle Java 8 in Ubuntu 16.04 Sum of real numbers that multiply to 1 I've seen a question in my math book with this explanation above it: "If the product of n positive real numbers is 1, then the sum of these numbers must be more than n". I was wondering if this is correct, and if it is, could someone give an explanation or a proof for it? I have a ASUS R500A notebook.Original OS is Windows 7 64bit.Few days ago I tried to Install Windows 8.1 64 bit version.But it failed &amp; error message is,     windows cannot be installed on this disk. The selected disk is of the GPT partition style.   My Steps: First i Deleted C: Partition ( Already installed windows 7 ). Then i Formatted that partition. Tried to install Windows 8.1 64bit.  In this hard disk i have another several partitions with Important data.  How do i Install Windows 8.1 without loosing Data from the Other partitions ? Cannot find Background Images feature in Blender 2.8 How can I recursively delete all files of a specific extension in the current directory? How do I safely delete all files with a specific extension (e.g. .bak) from current directory and all subfolders using one command-line? Simply, I'm afraid to use rm since I used it wrong once and now I need advice. How can I SELECT rows with MAX(Column value), PARTITION by another column in MYSQL? My table is:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   3 10 03/03/2009 john 300   4 11 03/03/2009 juliet 200   6 12 03/03/2009 borat 500   7 13 24/12/2008 borat 600   8 13 01/01/2009 borat 700     I need to select each distinct home holding the maximum value of datetime. Result would be:     id home datetime player resource     1 10 04/03/2009 john 399   2 11 04/03/2009 juliet 244   5 12 04/03/2009 borat 555   8 13 01/01/2009 borat 700     I have tried: -- 1 ..by the MySQL manual:   SELECT DISTINCT   home,   id,   datetime AS dt,   player,   resource FROM topten t1 WHERE datetime = (SELECT   MAX(t2.datetime) FROM topten t2 GROUP BY home) GROUP BY datetime ORDER BY datetime DESC  Doesn't work. Result-set has 130 rows although database holds 187. Result includes some duplicates of home. -- 2 ..join  SELECT   s1.id,   s1.home,   s1.datetime,   s1.player,   s1.resource FROM topten s1 JOIN (SELECT   id,   MAX(datetime) AS dt FROM topten GROUP BY id) AS s2   ON s1.id = s2.id ORDER BY datetime   Nope. Gives all the records. -- 3 ..something exotic:   With various results. What are the effects of exceptions on performance in Java? Question:  Is exception handling in Java actually slow?  Conventional wisdom, as well as a lot of Google results, says that exceptional logic shouldn't be used for normal program flow in Java.  Two reasons are usually given,   it is really slow - even an order of magnitude slower than regular code (the reasons given vary),     and    it is messy because people expect only errors to be handled in exceptional code.     This question is about #1.  As an example,  describes Java exception handling as "very slow" and relates the slowness to the creation of the exception message string - "this string is then used in creating the exception object that is thrown. This is not fast."  The article  says that "the reason for this is due to the object creation aspect of exception handling, which thereby makes throwing exceptions inherently slow".  Another reason out there is that the stack trace generation is what slows it down.  My testing (using Java 1.6.0_07, Java HotSpot 10.0, on 32 bit Linux), indicates that exception handling is no slower than regular code.  I tried running a method in a loop that executes some code.  At the end of the method, I use a boolean to indicate whether to return or throw.  This way the actual processing is the same. I tried running the methods in different orders and averaging my test times, thinking it may have been the JVM warming up.  In all my tests, the throw was at least as fast as the return, if not faster (up to 3.1% faster).  I am completely open to the possibility that my tests were wrong, but I haven't seen anything out there in the way of the code sample, test comparisons, or results in the last year or two that show exception handling in Java to actually be slow.  What leads me down this path was an API I needed to use that threw exceptions as part of normal control logic.  I wanted to correct them in their usage, but now I may not be able to.  Will I instead have to praise them on their forward thinking?  In the paper , the authors suggest that the presence of exception handlers alone, even if no exceptions are thrown, is enough to prevent the JIT compiler from optimizing the code properly, thus slowing it down.  I haven't tested this theory yet. When I use the , do I choose the monster to distract (and then the next ally to attack gets advantage) or do I choose the ally and the monster (so that only his attack against that target gets advantage)? Or something else?  Help [...] Alternatively, you can aid a friendly creature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally’s attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage. How can I calculate what the effect of an extension tube will be? Why is mathematical induction a valid proof technique? How to zoom in & zoom out While using 10.04 and the previous versions I used to put Ctrl+F6 to zoom in and subsequently Ctrl+F7 to zoom out. Now (using 11.10, Unity) I can't even find the options to zoom in and zoom out in the "keyboard shortcuts". I tried "the Magnifier" in the Compiz but really can't understand what is going on right there. There is simple question I would like to ask:   What to do so as to be able to zoom in with Ctrl+F6 and zoom out with Ctrl+F7? Get URL of ASP.Net Page in code-behind Auto reply to text and/or iMessage? Is it possible to set up an auto-reply to an incoming text or iMessage, either on my iPhone (or the connected Message app on my Mac)?  Ideally I'd like to customize this depending upon the sender. Word for "scary thing that's about to occur"? I have the feeling I'm forgetting a very simple word. But anyway, is there a word for that? Example:     The [...] that haven't occurred yet are the most scary ones. SQL Server: Examples of PIVOTing String data Trying to find some simple SQL Server PIVOT examples.  Most of the examples that I have found involve counting or summing up numbers.  I just want to pivot some string data.  For example, I have a query returning the following.  Action1 VIEW   Action1 EDIT   Action2 VIEW   Action3 VIEW   Action3 EDIT     I would like to use PIVOT (if even possible) to make the results like so:  Action1 VIEW EDIT   Action2 VIEW NULL   Action3 VIEW EDIT     Is this even possible with the PIVOT functionality?