Ban user for continuously asking questions which show no effort
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Suppose we have a set  $S=\{a,b\}.$ Obviously, the total number of binary operations on $S$ is the number of all the pairs such that $$*(a,b)=a \, \text{or}  \, b,$$ which gives  $ 2 \cdot 2 \cdot 2 \cdot 2=2^4$ possible ones. Is there a way to find which of these $16$ binary operations are associative without writing all the operation matrices and checking it by hand? Why do the directories /home, /usr, /var, etc. all have the same inode number (2)? What the #$@&%*! is that called? Is there a name for the use of symbols in place of curse words, for example #$@&amp;%*!? ERD for a web development company I am working on an ERD which represents the relationships between entities in a Web development company behavioral model. There I have entities like:   Customer Service ----------- (like: web development, web design, web consultation, ...) Order-item ------- (like: web development, web design, web consultation, ...) Order Invoice Project Project-phase Task --------------- (like: web development task3, web design task7) Developer Delivery ----------- (like: the developed web app, web consultation session, ...)   I have this diagram so far, though I know it still has major problems, and it is just for a start point:    Main concept   Customer makes order-items on services, combined to form an order which relates to an invoice. Each project has multiple project-phases with each project-phase related to an order. Each project-phase has multiple tasks, each of which is assigned to a developer. Each project-phase has a delivery, which will be delivered upon payment of the related orders invoice.   Questions   Are has and contains completely the same? If not, how to choose between them for relationships?! what is the measure?! Are there any rational problems with the Main concept section? Any helpful ideas or suggestions to improve this model?   Any help with this, would be really appreciated.  Update 1  Refined version of the diagram     Update 2  Considering an analogy of a Fast food restaurant would be helpful:   Customer ---------- A hungry person Service ------------- Making a burger, Home delivery, Mobile delivery, ... Order-item --------- A burger, ... Order ---------------- A home-delivered burger Invoice -------------- The printed invoice Project -------------- Serving the customer for a complete year (like a contract) Project-phase ----- Serving the customer for a single day Task ----------------- Preparing the kitchen, process the meat, ... Developer ---------- The cookie Delivery ------------- A burger in wrapped in wax papaer and a drink with the tray   Update 3  ()     Project seems to be unrelated to Customer in your diagram. Is this what you intended?   I think Order is and Project should not be related, as I think it is something off-the-counter and customer has nothing to do with it. she/he is only after the delivery and is concerned about time and money, nothing else. Please tell if I am wrong.     Are all Orders part of a Project or can you have orders that aren't in a project at all?   All Orders are part of a project, except those new ones which are waiting in the process queue.     Similarly, you relate order item directly to customer, but also to order. Are orders split between customers?   Please think of Order-Item as these:   web design web design consultancy domain name consultancy ...   So, customer choose some of these items, collected as an Order which has an invoice and could be paid. Order-Items are directly related to offered Services. I don't understand what do you mean by Are orders split between customers?.     If not you don't need a ternary relationship between customer, order item and service. Rather, an order item is an intersection between order and service. Order items belong to customers by inheritance from order (or even project?)   This is somehow true: Order items belong to customers by inheritance from order, but I think it is more rational to say it like this:     Order-Items, inherited from Service, belong to Order which itself belongs to Customer. There is a $C > 0$ such that $\vert f(z)-f(w)\vert \leq C\vert z-w\vert$ for a holomorphic map into $B(0, R)$. Let $0&lt;\delta&lt;r$ and $R&gt;0$, and $a\in\mathbb C$. I want to show that there exists $C&gt;0$ such that for all holomorphic functions $f\colon B(a,r)\to B(0,R)$, we have $$ \vert f(z)-f(w)\vert\leq C\vert z-w\vert $$ for $z,w\in B(a,\delta)$.  I'm not sure how to approach this. I was wondering if I could use that $$ \left\vert\frac{f^{(n)}(a)}{n!}\right\vert\leq\frac{\Vert f\Vert_{C(a,\rho)}}{\rho^n} $$ for some $0&lt;\rho&lt;r$. I also have an expression from biholomorphic maps from $B(0,1)$ to itself, but I'm not sure if I could use that here. Any hints? I have some data which looks like:  sampleA    ATGC    10   100 sampleA    ATGC    120  230 sampleA    ATGC    200  110   I want to print the min and max using the values in both column 3 and 4. So my output should look like:  sampleA   10  230   Thanks in advance If a and b are relatively prime and ab is a square, then a and b are squares. If $a$ and $b$ are two relatively prime positive integers such that $ab$ is a square, then $a$ and $b$ are squares.   I need to prove this statement, so I would like someone to critique my proof. Thanks  Since $ab$ is a square, the exponent of every prime in the prime factorization of $ab$ must be even.   Since $a$ and $b$ are coprime, they share no prime factors.   Therefore, the exponent of every prime in the factorization of $a$ (and $b$) are even, which means $a$ and $b$ are squares. How to set the fully qualified hostname on CentOS 7.0? How do I set the fully qualified hostname on CentOS 7.0?  I have seen a few posts online for example using:  $ sudo hostnamectl set-hostname nodename.domainname   However, running domainname returns nothing:  $ domainname (none)   Also:  $ hostname nodename.domainname   However,  $ hostname -f hostname: Name or service not known $ hostname -d hostname: Name or service not known   Some debug output:  $ cat /etc/hostname nodename.domainname  $ grep ^hosts /etc/nsswitch.conf hosts:      files dns I want Ctrl+Alt+B bring up a browser.  Ctrl+Alt+Delete is handy.  Can I set up Ctrl+Alt+B to bring up a browser (either default or specific)? Obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ where $\theta_{1}$ and $\theta_{2}$ are i.i.d $\text{Uniform}[0, 2\pi)$ I have 2 i.i.d Uniform random variables $\theta_{1}$ and $\theta_{2}$ on $[0, 2\pi)$. Here the problem pushes us to consider that all operations are made modulo $2\pi$. My question is how to obtain the joint PDF of $\theta_{1} - \theta_{2}$ and $\theta_{1}$ and then obtain the conditional PDF of $\theta_{1}$ given $\theta_{1} - \theta_{2}$??. For the second part It can be deduced from the first by writing it as the joint PDF divided by the PDF of $\theta_{1}$. But for the first part, A common idea that I saw is to derive the $\text{CDF}(x, y) = P(\theta_{1} - \theta_{2} \le x$, $\theta_{1} \le y$) and then perform derivations respect to $x$ and $y$. Is this a right approach? If yes, how to proceed with CDF especially with our uniform distribution restrictions? The following will cause infinite recursion on the == operator overload method      Foo foo1 = null;     Foo foo2 = new Foo();     Assert.IsFalse(foo1 == foo2);      public static bool operator ==(Foo foo1, Foo foo2) {         if (foo1 == null) return foo2 == null;         return foo1.Equals(foo2);     }   How do I check for nulls? Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$ Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$.  My Attempt: $$=\lim_{y\to 0} \dfrac {(x+y) \sec (x+y) - x\sec x}{y}$$ $$=\lim_{y\to 0} \dfrac {x\sec (x+y) + y\sec (x+y) - x\sec x}{y}$$ $$=\lim_{y\to 0} \dfrac {x(\sec (x+y) - \sec x) + y\sec (x+y)}{y}$$ msbuild, defining Conditional Compilation Symbols I'm possibly just blind, but is there a command line to specify conditional compilation symbols in MSBUILD?  I currently have this Line in my buildscript:  SET MSBUILD=C:\WINDOWS\Microsoft.NET\Framework\v2.0.50727\MSBuild.exe SET CONFIG=Debug %MSBUILD% /p:Configuration=%CONFIG% /p:OutputPath=..\..\output source\MyProject\MyProject.csproj   And I'd like to add a condition. In Visual Studio, i can just go into Project Properties => Build => Conditional compilation symbols, but I have not seen that option for msbuild?  Bonus Karma if you know if I can completely override all symbols already specified in the .csproj files to make sure that only the conditionals from my Buildscript go in. Could 'cogito ergo sum' possibly be false? What is the difference between currying and partial application? I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.  I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.  Could someone provide me with a definition of both terms, and details of how they differ? Read MIME data using PHP When a sentence uses a parenthetical plural, should the rest of the sentence treat it as singular or plural? As the title says: Is a 1st-level spell cast using a 4th-level slot a 1st-level spell, or a 4th-level spell? If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere I have been thinking on and off about a problem for some time now. It is inspired by an exam problem which I solved but I wanted to find an alternative solution. The object was to prove that some sequence of functions converges weakly to zero in $L^2$.   I managed to show (with some help) that the limit $f$ (of a subsequence) satisfies $\int_0^x f \ dm=0$ for all $x&gt;0 $. From this I want to conclude that $f=0$ a.e. I can do this with the fundamental theorem of calculus in its Lebesgue version but there ought to be a more elementary proof.  Can someone here help me out? What good CAD programs are available?