In Kill Bill (I think that is what the movie is called)**Hanzo breaks a 28 year old oath and makes the best in sword he's ever made for someone he doesn't even know just because she wants to kill Bill.  Why?*
During kill Bill, we learn that all the black mamba had to do to get Hanzo to build her a sword, was to mention Bill's name.  When black mamba meets Bill at the end, she tells him that all she did was mention his name. Bill responds with, "that'll do it!"  So what was it that Bill did to Hanzo to make him come out of retirement and make another weapon of death?
Where to start learning Linear Algebra? I'm starting a very long quest to learn about math, so that I can program games. I'm mostly a corporate developer, and it's somewhat boring and non exciting. When I began my career, I chose it because I wanted to create games.  I'm told that Linear Algebra is the best place to start. Where should I go? What are the technical obstacles that doesn't allow OSX to be installed in a PC? What's the difference between an id and a class? How to know when to change a chain? A bike shop employee used a tool he said would check the wear on the chain, and said that it should be changed.   He said it took a measurement that meant the chain had expanded, but it is still hard for me understand why I should change the chain.   He said that the reason was that the expanded chain links will cause the chain rings to wear down.   That is one argument and I have no experience with it, to know if it is true.   But are there more reasons? How do I know when the chain should be changed?   My first thought is to use it until it breaks, but it probably is not the wisest option. Baked beans still firm after soaking and hours of cooking What is the difference between correlation and causation? What is the difference between correlation and causation?  Pirates and Global Temperature Example  For example, how do we know when we're dealing with correlation only and not also causation here?   What Certain Philosophers Seem to Hold Regarding This  It would seem that   Hume would saycorrelation ≡ causation. Aristotle would say that in generalcorrelation ≢ causationand thatcausation ⇔ correlationonly if we are not dealing with chance events.   ("≡" means "is identical to," and "⇔" means "implies each other.") If $|G/H|=4$ then $G$ is union of three proper subgroups Let $G$ be a finite group and $N$ a normal subgroup of $G$ of index $4$. Prove that $G$ has a subgroup of index $2$ (hence normal) and if $G/H$ is not cyclic then $G$ is equal to the union of three proper subgroups.   I understand that $G/H$ is isomorphic to $\mathbb{Z}_4$ or $\mathbb{Z}_2\times \mathbb{Z}_2$. Let $K^*$ be a subgroup of $G/H$ of order $2$. Then $K^*\cong K/H$ for some $K$ such that $H$ is normal in $K$ and hence $[G:K]=[G/H:K/H]=4/2=2$.  If $G/H$ is not cyclic then $G/H\cong \mathbb{Z}_2\times \mathbb{Z}_2$. I don't know how to prove $G$ is the union of three subgroups. Could it be true that as $G/H$ is the union of three proper subgroups $K_1^*,K_2^*,K_3^*$ then the corresponding groups $K_1,K_2,K_3$ have union equal to $G$? Would anyone give me a hint to prove this?  Thank you. I am using XeLaTeX and memoir to write a longer text with several parts, chapters and sections. When printing the \tableofcontents I get a spacing problem with 2-figure numbers almost overlapping the relevant section name, as per enclosed picture.  I am aware that the memoir manual has a section dedicated to this theme, but the most part of it is doubledutch to me. Is there any easy way to avoid this problem? I see this often in the build scripts of projects that use autotools (autoconf, automake).  When somebody wants to check the value of a shell variable, they frequently use this idiom:  if test "x$SHELL_VAR" = "xyes"; then ...   What is the advantage to this over simply checking the value like this:  if test $SHELL_VAR = "yes"; then ...   I figure there must be some reason that I see this so often, but I can't figure out what it is. When calling super() in a derived class, can I pass in self.__class__? The Help Vampire problem SQL to generate a list of numbers from 1 to 100 So I'm getting my listItems with a Camlquery, but i want to calculate the avg of the "price" rows  This is the code I've used so far:  function VisaLista() {     namn = document.getElementById("txtNamn");     var camlQuery = new SP.CamlQuery();     camlQuery.set_viewXml(     "&lt;Where&gt;" +     "&lt;And&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Title'/&gt;&lt;Value Type='Text'&gt;" + namn + "&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Or&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Prioritet'/&gt;&lt;Value Type='Text'&gt;Hög&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;Eq&gt;&lt;FieldRef Name='Status'/&gt;&lt;Value Type='Text'&gt;Startad&lt;/Value&gt;&lt;/Eq&gt;" +     "&lt;/Or&gt;" +     "&lt;/And&gt;" +     "&lt;/Where&gt;");     listItems1 = list.getItems(camlQuery);     clientContext.load(listItems1);     clientContext.executeQueryAsync(OnSuccessVisa, OnFail); } function OnSuccessVisa() {     var listEnumerator = listItems1.getEnumerator();     var elmt = 0;     while (listEnumerator.moveNext()) {         var currentItem = listEnumerator.get_current();         elmt = (currentItem.get_item('_x0072_zb6'));          var sum = 0;         for (var i = 0; i &lt; elmt.length; i++) {             sum += parseInt(elmt[i], 10);         }          var avg = sum / elmt.length;          document.write("The sum of all the elements is: " + sum + " The average is: " + avg);     }     $("#Kategori1").text = "Medelvärdet för dessa ordrar: " + avg }   I am getting following error     "Cannot get the value length of null - at elmt, line 43 $\mathbb Z[\sqrt 3]$ contains infinitely many units When I look at the black and white photographs from professional photographers, I notice that they have a special look. Not a specific style—obviously each photographer has her own style—but a look which make them different from similar color photos, a special feeling, which makes them shine specifically as black and white and makes color irrelevant.  When I convert my own photos to black and white in Lightroom, they don't have any special look. They just look like any other of my photos, simply converted to black and white. I imagine that there are two reasons for that:   Some scenes are better for black and white. Talented and/or experienced photographers know which scenes would be beautiful in black and white, and shoot specifically those scenes. Moreover, they know how to adapt the scene itself and the lighting to black and white (for instance by not relying on the color contrast itself).  In my case, I don't think much about shooting for black and white. It comes only in post-processing, when I either think that the photo will look great in black and white (and very often, it doesn't), or I find the colors to be poor and turn the photo to black and white (which actually doesn't make the photo any better). Post-processing is much more complex than clicking on black and white button in an app. It involves not only adjusting black and white mix (i.e. raising or lowering the lightness of specific colors), but doing lots of other adjustments.  In my case, I do black and white mix, but other adjustments I do are similar to what I would do for a color photo: actually, I may even do them on a color photo, and only then turn it to black and white.   So, what should I take in account if I want to have decent black and white photographs? Are there specific techniques, tips, tricks or warnings for someone who usually shots in color and wants to start black and white photography?  Let me show some examples. Are those scenes not great for black and white photos in the first place? Or can they be salvaged through proper post-processing?  1.  First, a poorly done photo from Scotland with dubious composition and very poor colors that I was unable to correct in Lightroom.  The same image in black and white isn't much better. The difference between the trees and the grass on the hill is barely visible. Houses on the hill fade with the sky much more than in the original version.      2.  Here's a photo of a cute pet.  In black and white, the gap between the mouse's ear and the background is barely visible. There is absolutely no benefit compared to the original.      3.  Finally, an example of a much more contrasty picture. The black and white version is weird, since the lack of color makes it difficult to understand whether the soil is the actual sand or something else. I find the sky to be weird as well, and making the blue channel darker or lighter in Lightroom haven't changed that. Splitting of primes in the compositum of fields If $L_i/K$ are Galois extensions of number fields, $i=1,\ldots,n$, and $L=L_1\cdots L_n$ is the compositum. Then it's true that a prime $\mathfrak{p}$ of $K$ splits in $L$ if and only if it splits in all of $L_i$. Does this also hold if the $L_i$ are not Galois extensions of $K$?  The proof that I know regarding the compositum uses the fact that the $L_i/K$ are Galois, so is this true in the more general setting and how would one prove it? The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property? Would approaching a distant star at near the speed of light unfold its entire history in "fast-forward"? A standard proof for press needs crop marks and color bars as below    With the package crop, the crop marks can be easily added.  But how about the color bar ?  Is there a way or a package to make it ?  An example is   \documentclass[b5paper,10pt]{article} \usepackage[utf8]{inputenc} \usepackage[cross,a4,center,info,axes]{crop}  \title{Test} \author{User} \begin{document} \maketitle \section{Fox} The quick brown fox jumps over a lazy dog. \end{document} Proof for triangle inequality for vectors Generally,the length of the sum of two vectors is not equal to the sum of their lengths. To see this consider the vectors $u$ and $v$ as shown below.  By considering $u$ and $v$ as two sides of a triangle, we can see that the lengths of the third side is $\| u + v \|$ and we have $\| u + v \| \leq \|u\| + \|v\|$.  Under what circumstance equality occurs and how can one prove that?