Units of $\mathbb Z[\sqrt 3]$
$\mathbb Z[\sqrt 3]$ contains infinitely many units
Grammar of "supposed to": part of speech / word class, active or passive? If I say     I'm supposed to go.   Is supposed to here an adjective in a passive construction? Why does k-means clustering algorithm use only Euclidean distance metric? Is there a specific purpose in terms of efficiency or functionality why the k-means algorithm does not use for example cosine (dis)similarity as a distance metric, but can only use the Euclidean norm? In general, will K-means method comply and be correct when other distances than Euclidean are considered or used?  [Addition by @ttnphns. The question is two-fold. "(Non)Euclidean distance" may concern distance between two data points or distance between a data point and a cluster centre. Both ways have been attempted to address in the answers so far.] What level are spells cast at if a warlock multiclasses as another caster? "Improve" treated as improper response to proper response to audit What is the minimum wait before I may re-enter the USA after a 90 day visit on the Visa Waiver Program? I entered the USA on a three month visa waiver program from Australia. I am about to return to  Australia and would like to come back again to the USA. How long do I have to wait until I can re-enter the USA for another 3 months? Java string to date conversion WIth Vimeo Plus account, how to hide/remove the "play" button in the middle of an embedded video? Why is one migration showing up as to a blank site? I was just looking at the statistics for migrated questions in the  mod tools, and noticed this oddity:    The actual statistics, as visible to any 10k+ SFF user , are: 6 migrated to Worldbuilding, 2 to Literature, 2 to SFF meta, 1 to Movies &amp; TV, 1 to Writers, and 1 to Aviation.  Why is one of the meta migrations showing up with a blank icon rather than with the other?  Both migrated questions were closed as duplicates on meta. Both were migrated by 5 community members without mod involvement. One of the stubs on main has since been deleted, but so have the stubs for some of the other migrated questions. I can't think of anything to explain this discrepancy. Italics/roman in BibTeX I use a BibTeX style which automatically italicises booktitles (using \emph). I have certain entries which contain italicised words in the title. I would like these to appear non-italicised (in roman) in the final PDF output. Using any of \emph or \textit or \textrm on these items doesn't seem to make any difference -- the whole title still appears in italics.  Minimal .bib entry  @PHDTHESIS{klein1974, author = {Klein, Jared S.}, title = {The Particle \emph{u} in the {R}igveda}, school = {Yale}, year = {1974}, address = {New Haven, CT}, timestamp = {2009.12.04} }   Minimal .bbl entry generated by sp.bst:  \bibitem[{Klein(1974)}]{klein1974} Klein, Jared~S. 1974. \newblock \emph{The particle \emph{u} in the {R}igveda}. \newblock New Haven, CT: Yale dissertation. Do Stack Overflow and other Stack Exchange sites have an app I can use? I like using Stack Overflow (or any other Stack Exchange sites) and was wondering if there was an app I could install on my phone or other device that would allow me to use the site on-the-go or straight from my desktop.  Some systems to consider:   Windows 8 Android iPhone/iOS   What are some apps that I could install to my computer or phone to enhance my Stack Exchange experience? For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge? Combining two expressions (Expression>) I'm starting  and finally decided to learn how to write epsilon-delta proofs.  I have been working on chapter 5, number 3(ii). The problem, in essence, asks to prove that     $$\lim\limits_{x \to 1} \frac{1}{x} = 1.$$    Here's how I started my proof,     $$\left| f(x)-l \right|=\left| \frac{1}{x} - 1 \right| =\left| \frac{1}{x} \right| \left| x - 1\right| &lt; \epsilon \implies \left| x-1 \right| &lt; \epsilon |x|$$   I haven't made any further progress past this point. Is it possible to salvage this proof? Should I try an alternate approach? How to set scale across all blender objects and keyframes? Why is uniq ignoring Unicode and lines with a single letter? I'm trying to combine both the American and British dictionaries into one large dictionaries, and I'm trying to remove all the duplicates from the superset, but it seems that uniq is not outputting words like, "épée" or single letters.  This is what I've tried using:  LC_COLLATE=en_US.UTF-8 cat american-english british-english |sort|uniq -u &gt; unique_sorted_combined_dict   If I just do this:  LC_COLLATE=en_US.UTF-8 cat american-english british-english |sort &gt; sorted_combined_dict   "épée" and other such words do show up, along with single letters.  Is there something I'm missing here with uniq?  I should note that I'm using uniq from the GNU coreutils on Ubuntu 12.10, if that makes any difference. How can I assign a Func conditionally between lambdas using the conditional ternary operator? Generally, when using the conditional operator, here's the syntax:  int x = 6; int y = x == 6 ? 5 : 9;   Nothing fancy, pretty straight forward.  Now, let's try to use this when assigning a Lambda to a Func type. Let me explain:  Func&lt;Order, bool&gt; predicate = id == null     ? p =&gt; p.EmployeeID == null     : p =&gt; p.EmployeeID == id;   That's the same syntax, and should work? Right? For some reason that doesn't. The compiler gives this nice cryptic message:     Error  1   Type of conditional expression cannot be determined because there is no implicit conversion between 'lambda expression' and 'lambda expression'   I then went ahead and changed the syntax and this way it did work:  Func&lt;Order, bool&gt; predicate = id == null     ? predicate = p =&gt; p.EmployeeID == null     : predicate = p =&gt; p.EmployeeID == id;   I'm just curious as to why it doesn't work the first way?  (Side note: I ended up not needing this code, as I found out that when comparing an int value against null, you just use object.Equals) Verify is tautology by using logical equivalence Verify is tautology by using logical equivalence:  $$((p ∨ q) ∧ (p → r) ∧ (∼ r)) → q$$  by showing what laws are using, step by step explanation needed.  Logical equivalence: de morgan's laws, commutativity, associativity, double negative, distribution, idempotent, absorption, identity, universal bound, negation  Rules of inference: modus ponens, modus tollens, generalisation, specialisation, conjunction, ellimination, transivity, proof by division into cases, contradiction  What I got so far:  I need to prove   $$((p ∨ q) ∧ (p → r) ∧ (∼ r)) → q ≡ \text{tautology}$$ Since $p → r$ same as $∼ p ∨ r$: $$((p ∨ q) ∧ (p → r) ∧ (∼ r)) → q ≡ ((p ∨ q) ∧ (∼ p ∨ r ) ∧ (∼ r)) → q$$  I am stuck here Initialize class fields in constructor or at declaration? I've been programming in C# and Java recently and I am curious where the best place is to initialize my class fields.  Should I do it at declaration?:  public class Dice {     private int topFace = 1;     private Random myRand = new Random();      public void Roll()     {        // ......     } }   or in a constructor?:  public class Dice {     private int topFace;     private Random myRand;      public Dice()     {         topFace = 1;         myRand = new Random();     }      public void Roll()     {         // .....     } }   I'm really curious what some of you veterans think is the best practice. I want to be consistent and stick to one approach. I get this warning:     Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and will likely be removed in a future release   What does it mean? How to control fan speed? How can I control the computer's fan speed?  On Windows there is a wonderful program called .