What's the correct way to write that a functions is not defined?  e.g.  $$ \begin{bmatrix} a &amp; b &amp; c\\ d &amp; e &amp; f \\  \end{bmatrix} \begin{bmatrix} x\\ y \\  \end{bmatrix} \text{is not defined}  $$  or  $$ \frac10 \text{is undefined} $$
Consider a partial function $f$ that is defined only for a few values of its domain (my exact use case is $\delta$ transition functions in automata). One can 'complete' it by saying $$g(x)=0\iff f(x) \text{ is not defined.}$$  Is there a symbol to mean "undefined"? Would it be correct, or accurate, to write $\nexists f(x)$?
Benefits of using QQ-plots over histograms In , Nick Cox wrote:     Binning into classes is an ancient method. While histograms can be useful, modern statistical software makes it easy as well as advisable to fit distributions to the raw data. Binning just throws away detail that is crucial in determining which distributions are plausible.   The context of this comment suggests using QQ-plots as an alternative means to evaluate the fit. The statement sounds very plausible, but I'd like to know about a reliable reference supporting this statement. Is there some paper which does a more thorough investigation of this fact, beyond a simple “well, this sounds obvious”? Any actual systematic comparisons of results or the likes?  I'd also like to see how far this benefit of QQ-plots over histograms can be stretched, to applications other than model fitting. Answers on  agree that “a QQ-plot […] just tells you that "something is wrong"”. I am thinking about using them as a tool to identify structure in observed data as compared to a null model and wonder whether there exist any established procedures to use QQ-plots (or their underlying data) to not only detect but also describe non-random structure in the observed data. References which include this direction would therefore be particularly useful. Difference of $R^2$ between OLS with individual dummies to panel fixed effect model? Based on my understanding, panel fixed effect model is equivalent to OLS with individual dummies. However, when I ran the two models in R, the $R^2$ from the two models were quite different: 0.8 for OLS with individual dummies and 0.06 for fixed effect model.  Is it the case that in fixed effect model, the fixed effects (individual dummies) are excluded from the calculation of $R^2$? What is the maximum value of $n$ if $n + 5$ divides $n^5 + 5$, $n$ being a natural number? I tried to solve by binomial theorem but it failed. How to use a custom time in browser to test for client vs server time difference What does $(command) & do? Find the probability that a geometric random variable $X$ is an even number Are the off-world colonies really a "golden land of opportunity"? In Blade Runner, there seems to be quite a  for emigration to the off-world colonies, e.g.,      "A new life awaits you in the off-world colonies, a chance to begin   again in a golden land of opportunity and adventure."   Is there any evidence that people emigrating are actually better off than staying on Earth?  The job descriptions of the replicants Deckard is tasked with "retiring" don't seem consistent with the colonies being wonderful places. If the colonies offered a good life, would they have to do so much advertising? Why doesn't C# support implied generic types on class constructors? C# doesn't require you to specify a generic type parameter if the compiler can infer it, for instance:  List&lt;int&gt; myInts = new List&lt;int&gt; {0,1,1,     2,3,5,8,13,21,34,55,89,144,233,377,     610,987,1597,2584,4181,6765};  //this statement is clunky List&lt;string&gt; myStrings = myInts.     Select&lt;int,string&gt;( i =&gt; i.ToString() ).     ToList&lt;string&gt;();  //the type is inferred from the lambda expression //the compiler knows that it's taking an int and  //returning a string List&lt;string&gt; myStrings = myInts.     Select( i =&gt; i.ToString() ).     ToList();   This is needed for anonymous types where you don't know what the type parameter would be (in intellisense it shows up as 'a) because it's added by the compiler.  Class-level type parameters don't let you do this:  //sample generic class public class GenericDemo&lt;T&gt;  {     public GenericDemo ( T value )      {         GenericTypedProperty = value;     }      public T GenericTypedProperty {get; set;} }  //why can't I do: int anIntValue = 4181; var item = new GenericDemo( anIntValue ); //type inference fails  //however I can create a wrapper like this: public static GenericDemo&lt;T&gt; Create&lt;T&gt; ( T value ) {     return new GenericDemo&lt;T&gt; ( value ); }  //then this works - type inference on the method compiles var item = Create( anIntValue );   Why doesn't C# support this class level generic type inference? In java SSL over https without certificate Closing a Java FileInputStream Quoted vs unquoted string expansion I would like to show that $a^n \mid b^n$ implies $a \mid b$  I thought I could convert it to congruences and work backwards, but as far as I remember, $a \equiv b \pmod{m}$ implies $a^n \equiv b^n \pmod{m}$, not the opposite, unless $m$ is prime. Is that right?  So I am not sure how to approach this one. Any ideas?  Thanks! Do the Manuals and Tomes allow you to exceed 20 in an ability score? And can they be stacked? I am looking at items like Manual of Bodily Health, Tome of Clear Thought, etc.  Quoting from Manual of Bodily Health     If you spend 48 hours ... your Constitution score increases by 2, as   does your maximum for that score.   This sounds to me like when you read the tome according to the instructions, you are then allowed to increase your CON up to a maximum of 22.     Is that a correct reading -- that these magic items allow a player to override the usual ability score maximum of 20? Probably, you were already at 20 when you read it, but if, say, you were at 18 and read it to bring your CON up to 20, could you then later increase your CON further via feats or ability score increases gained at certain levels? Can you read more than one book of the same type, to increase your maximum by an additional 2 points? Why $\gcd(qb+r,b)=\gcd(b,r)$? Coordinate descent soft-thresholding update operator for LASSO I was reading this paper () describing the coordinate descent algorithm for LASSO, and I can't quite figure out how the soft-thresholding update for each $\beta_j$ is derived for the linear regression case. Specifically, how does one go from equation (4) to equation (5) in the paper? Can anyone show me a detailed derivation of the update? Thanks!  Edit: actually this paper deals with the elastic net penalizing term, which reduces to LASSO when $\alpha=1$. I am mostly interested in LASSO, but I guess the derivation should be principally the same for elastic net. How can I detect the encoding/codepage of a text file In our application, we receive text files (.txt, .csv, etc.) from diverse sources. When reading, these files sometimes contain garbage, because the files where created in a different/unknown codepage.  Is there a way to (automatically) detect the codepage of a text file?   The detectEncodingFromByteOrderMarks, on the StreamReader constructor, works for UTF8  and other unicode marked files, but I'm looking for a way to detect code pages, like ibm850, windows1252.     Thanks for your answers, this is what I've done.  The files we receive are from end-users, they do not have a clue about codepages. The receivers are also end-users, by now this is what they know about codepages: Codepages exist, and are annoying.  Solution:    Open the received file in Notepad, look at a garbled piece of text. If somebody is called François or something, with your human intelligence you can guess this. I've created a small app that the user can use to open the file with, and enter a text that user knows it will appear in the file, when the correct codepage is used.  Loop through all codepages, and display the ones that give a solution with the user provided text.  If more as one codepage pops up, ask the user to specify more text. Sql Server 'Saving changes is not permitted' error ► Prevent saving changes that require table re-creation I installed the  on my Ubuntu&nbsp;11.04 (Natty Narwhal) with   sudo apt-get install lamp-server^   Now I navigate to /var/www and use   wget http://ftp.drupal.org/files/projects/drupal-7.x-dev.tar.gz   I get the following error.   --2011-08-03 13:59:00--   http://ftp.drupal.org/files/projects/drupal-7.x-dev.tar.gz Resolving  ftp.drupal.org... 64.50.233.100, 64.50.236.52 Connecting to  ftp.drupal.org|64.50.233.100|:80... connected. HTTP request sent,  awaiting response... 200 OK Length: 2757101 (2.6M)  [application/x-gzip] drupal-7.x-dev.tar.gz: Permission denied   Cannot write to `drupal-7.x-dev.tar.gz' (Permission denied).   How do I resolve this error?  I tried to download the same file in the downloads folder, and it went on without an issue. So it seems to be some permission error, but I'm not sure about that or how to solve it. How can I find out where an email really came from? Spam iCloud Calendar Invitations