The obvious response is $A = B$. But I came up with another response. I can't figure out what's my bias.  Lets say    $S = A - B$ $T = B - A$   Proving $S=T$ means proving $S \subseteq T$ and $T \subseteq S$  Let's start with $S \subseteq T$  For any $x \in S$ :   $x \in A$ $x \notin B$   if $S \subseteq T$, $x \in T$ and :    $x \in B$ $x \notin A$   There is no $x$ giving satisfaction, so $A$ and $B$ are empty.  I prove $T \subseteq S$ by symmetry  My solution is : $A = B = \emptyset$  What's wrong ?
Hello I am taking a Discrete Mathematics course and having some trouble with this question about sets:  Under what conditions is $A- B = B- A$  Diagram:   Diagram:   Maybe I'm understanding incorrectly, but how can A-B and B-A be equal if they contain elements that are not in each other?
Why am I getting "No such file or directory" when I try to execute a binary? Is "of" instead of "have" correct? Magic leaves "smudges" and a sorceress becomes a book I could use some help identifying a book I read some time in the last year or so. The book goes between two different stories:  1) A student of magic finds a book in a cave that turns out to be a person transformed into a book. The book talks to the student and they share thoughts. At some point, the student runs away, chase ensues, and at the very end of the book, he manages to travel to another plane.  2) A girl in a religious society where magic is forbidden. She is the daughter of painters. She discovers she can see magic. Falls in love with some random painter, risks performing magic to not be pregnant, does it again so she can, and is arrested and sent to some prison thing.  The common element between the stories is that magic use leaves behind a smudge of some kind that can be visible.  Any assistance is appreciated. Record Animation In BGE Execute shell script or command on idle time I'm searching for the possibility to execute a shell script or command based on idle time in the bash shell.  As an example, if I'm in a SSH session to a server of mine and after X minutes of inactivity in the terminal, I want a command to start a desired program like cmatrix, and when I come back and press a key I will get back where I left. According to , if there is a potential difference, $V$, across a resistor then there is a current, $I$, flowing through it.   Since we assume that points along the connecting wire are at the same potential, how can current, $I$ flow between points at the same potential, $V$? Could gravity accelerate light? Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still apply to light? The speed of light is constant, of course, but why are photons affected by gravity yet aren't accelerated by it?  Edit: My main question is why photons aren't affected in the same way as most other particles. I'm perfectly aware that it cannot surpass lightspeed, but I want to know what makes it unaffected by acceleration while other particles are affected. Suppose $A$ is a $n \times n$ constant matrix. How can I prove $\det(e^A) = e^{\displaystyle \sum_{\lambda_i\in\sigma(A)} \lambda_i}$,  where $\sigma(A)$ is the multiset of eigenvalues of $A$?  The following matlab code shows this is true in $n = 3$ case:  A = rand(3) detA = exp(sum(eig(A))) detmA = det(expm(A)) Let $A$ be a $m \times n$ matrix with entries from some field $F$. Define the determinant rank of $A$ to be the largest possible size of a nonzero minor, i.e. the size of the largest invertible square submatrix of $A$. It is true that the determinant rank is equal to the rank of a matrix, which we define to be the dimension of the row/column space.  It's not difficult to see that $\text{rank} \geq \text{determinant rank}$. If some submatrix of $A$ is invertible, then its columns/rows are linearly indepedent, which implies that the corresponding rows/columns of $A$ are also linearly indepedent.  Is there a nice proof for the converse? Why are map tiles being repeated? Using MapServer and Openlayers How to combine two jQuery results How do you combine two jQuery search results? eg:  var $allFoos = $('.foo'),     $allBars = $('.bar')     $allFoosAndBars = $allFoos + $allBars;   Obviously, I just made up that last line, but I hope it makes it sorta clear what I mean. To be clear, the example is greatly simplified, and it could be any arbitrary sets i'm talking about, so $('.foo, .bar') is not what I'm after. Here comes Bob.  Bob is coming here.  Would anyone please explain what is  the difference between these? Last night I was updating my Ubuntu 10.04 to either 11.04 or 12.04 (I'm not entirely sure which one it was, but I think it was 11.04) and I left it overnight to finish. When I came down in the morning, I noticed that the computer hadn't barely begun installing the updates! The update thing said that my computer was on the installation step, but it was still preparing the libc bin (or whatever its called) . It's like the first part of the step installing the upgrades. So, I stupidly restarted the computer, and when it rebooted, I got five options on a purple screen:  Ubuntu, with Linux 3.0.0-28-generic Ubuntu, with Linux 3.0.0-28-generic (recovery mode) Previous Linux versions Memory test (memtest86+) Memory test (memtest86+, serial console 115200)   Long story short, not matter which way I enter Ubuntu to try and reinstall the updates using the root thing (it's like terminal) after I enter sudo apt-get update it basically said it failed to fetch every url link, and it then says:  W: Some index files have failed to download. They have been ignored, or old ones used instead. W: Not using locking for read only lock file /var/lib/dpkg/lock E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem.   So, I entered sudo dpkg --configure -a, and it says:  dpkg: error: unable to access dpkg status area: Read-only file system"   I'm left like wtf, and I really just some guidance here. I just got this laptop, and I can not afford a new one if I broke this one. Is there a benefit to using one over the other? In Python 2, they both seem to return the same results:  &gt;&gt;&gt; 6/3 2 &gt;&gt;&gt; 6//3 2 Does Overhand Chop override the damage bonus from wielding a two handed weapon? I was showing a GM friend of mine a build I was making that uses the Two-Handed Fighter Archetype and we are both unsure of how it interacts with the damage bonus you get from two-handed weapons (which is 1-1/2 times your STR.) It reads:     Overhand Chop (Ex): At 3rd level, when a two-handed fighter makes a single attack (with the attack action or a charge) with a two-handed weapon, he adds double his Strength bonus on damage rolls. This ability replaces armor training 1.   So, does Overhand Chop turn the 1-1/2 times multiplier from two-handed weapons into a 2 times multiplier, or do the two add up? Or, do they interact in some other way?   This assumes a Medium sized character with 20 STR and a greatsword with 3 levels. Why we can't implement AES 512 key size? Out of curiosity why we can't implement AES 512 key size?    Please explain somehow i can understand! I'm not an expert. What was L's real name? I watched through Death Note once, and I never remember hearing L's name, even after he died.  What was L's real name, or did he never have one (it was never said)? "happen to be" and "happen to have" - expressions of probability? Based on Logman dictionary:       happen to do something: if you happen to do something, you do it by chance.   for example take a look at these examples:     They happen to be unemployed at the time. I happen to have a degree in computer science.    So based on the definition of the happen to do something, first one means they are probably unemployed at the time. and the second one means I probably have a degree in computer science.     Am I right? How do I free up more space in /boot? When voting to migrate an off-topic question, why is the list of sites limited?