cubic equation:  $$ax^3+bx^2+cx+d=0$$  Cube means 3.  Quadratic equation:  $$ax^2+bx+c=0$$  Quad means 4. But it is a power of two, should it be called bi... Equation.     My question is: Is this a mistake in naming the quadratic equation?
Why is it called a quadratic if it only contains $x^2$, not $x^4$? Should it not be bidratic or didratic etc?
Unable to correct problems, you have held broken packages Badge "multiplier" a little bit misaligned on the profile page Well, you can see it for yourself. The badge multiplier is a bit misaligned. Can you fix this please? (I know it's kinda a minor issue but it's bugging me and it's somehow off)    If it helps, I'm using Chrome version 44.0.2403.125 m. (Also repro'ed on FireFox 39.0 and )    For no good reason, that's a screenie from 's profile page. Historical reason behind different line ending at different platforms Why did DOS/Windows and Mac decide to use \r\n and \r for line ending instead of \n? Was it just a result of trying to be "different" from Unix?  And now that Mac OS X is Unix (-like), did Apple switch to \n from \r? There's a theorem of Kaplansky that states that if an element $u$ of a ring has more than one right inverse, then it in fact has infinitely many. I could prove this by assuming $v$ is a right inverse, and then showing that the elements $v+(1-vu)u^n$ are right inverses for all $n$ and distinct.  To see they're distinct, I suppose $v+(1-vu)u^n=v+(1-vu)u^m$ for distinct $n$ and $m$. I suppose $n&gt;m$. Since $u$ is cancellable on the right, this implies $(1-vu)u^{n-m}=1-vu$. Then $(1-vu)u^{n-m-1}u+vu=((1-vu)u^{n-m-1}+v)u=1$, so $u$ has a left inverse, but then $u$ would be a unit, and hence have only one right inverse.  Does the same theorem hold in monoids, or is there some counterexample? Should we host our own nameservers? This is a  about whether to outsource DNS resolution for ones own domains   I currently have my ISP providing DNS for my domain, but they impose limitations on adding records. Therefore, I am thinking about running my own DNS.  Do you prefer to host your own DNS, or is it better to have your ISP do this?  Are there alternatives which I can look into? Java map with values limited by key's type parameter Is there a way in Java to have a map where the type parameter of a value is tied to the type parameter of a key? What I want to write is something like the following:  public class Foo {     // This declaration won't compile - what should it be?     private static Map&lt;Class&lt;T&gt;, T&gt; defaultValues;      // These two methods are just fine     public static &lt;T&gt; void setDefaultValue(Class&lt;T&gt; clazz, T value) {         defaultValues.put(clazz, value);     }      public static &lt;T&gt; T getDefaultValue(Class&lt;T&gt; clazz) {         return defaultValues.get(clazz);     } }   That is, I can store any default value against a Class object, provided the value's type matches that of the Class object. I don't see why this shouldn't be allowed since I can ensure when setting/getting values that the types are correct.  EDIT: Thanks to cletus for his answer. I don't actually need the type parameters on the map itself since I can ensure consistency in the methods which get/set values, even if it means using some slightly ugly casts. Probability that the sum of 6 dice rolls is even What characters do I need to escape when using sed in a sh script? Take the following script:  #!/bin/sh sed 's/(127\.0\.1\.1)\s/\1/' [some file]   If I try to run this in sh (dash here), it'll fail because of the parentheses, which need to be escaped. But I don't need to escape the backslashes themselves (between the octets, or in the \s or \1). What's the rule here? What about when I need to use {...} or [...]? Is there a list of what I do and don't need to escape? c++ get registry key returns only one char For macro photography, how do I choose between a compact camera or a mirrorless interchangeable-lens camera (without considering a lens)?   What indicator(s) should I look for when making the choice? Beamer and description environment text size SQL group by day, show orders for each day I have an SQL 2005 table, let's call it Orders, in the format:  OrderID, OrderDate,  OrderAmount 1,       25/11/2008, 10 2,       25/11/2008, 2 3,       30/1002008, 5   Then I need to produce a report table showing the ordered amount on each day in the last 7 days:  Day,        OrderCount, OrderAmount 25/11/2008, 2,          12 26/11/2008, 0,          0  27/11/2008, 0,          0  28/11/2008, 0,          0 29/11/2008, 0,          0 30/11/2008, 1,          5   The SQL query that would normally produce this:  select count(*), sum(OrderAmount)     from Orders     where OrderDate&gt;getdate()-7     group by datepart(day,OrderDate)   Has a problem in that it will skip the days where there are no orders:  Day,        OrderCount, OrderAmount 25/11/2008, 2,          12 30/11/2008, 1,          5   Normally I would fix this using a tally table and outer join against rows there, but I'm really looking for a simpler or more efficient solution for this. It seems like such a common requirement for a report query that some elegant solution should be available for this already.   So: 1. Can this result be obtain from a simple query without using tally tables?  and 2. If no, can we create this tally table (reliably) on the fly (I can create a tally table using CTE but recursion stack limits me to 100 rows)? I'm trying to show that  $$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$  Where $a_{i}$ are the roots of the function $f(x)$. I've tried to proceed by using a dummy function $g(x)$ and carrying out:  $$\int_{-\infty}^{\infty}dx\,\delta\big(f(x)\big)g(x)$$  Then making the coordinate substitution $u$ = $f(x)$ and integrating over $u$. This seems to be on the right track, but I'm unsure where the absolute value comes in in the denominator, and also why it becomes a sum.  $$\int_{-\infty}^{\infty}\frac{du}{\frac{df}{dx}}\delta(u)g\big(f^{-1}(u)\big) = \frac{g\big(f^{-1}(0)\big)}{\frac{df}{dx}\big(f^{-1}(0)\big)}$$  Can any one shed some light? Wikipedia just states the formula and doesn't actually show where it comes from. UK visit visa: What documents prove genuine relationship with the visitor? In theory, is it possible that the loss on the train set will increase together with the train set accuracy? (in the normal case the train set loss should go down) And vice versa, can the train loss decrease along with the accuracy?   Note: This is obviously different than the classic underfit / overfit cases which are easier to grasp. How to know the types of windowing system, window manager and desktop environment of a Unix-like OS How can I reference the script element that loaded the javascript that is currently running?  Here's the situation. I have a "master" script being loaded high in the page, first thing under the HEAD tag.  &lt;!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"  "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"&gt; &lt;html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"&gt; &lt;head&gt; &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt;   There is a script in "scripts.js" which needs to be able to do on-demand loading of other scripts. The normal method doesn't quite work for me because I need to add new scripts without referencing the HEAD tag, because the HEAD element hasn't finished rendering:  document.getElementsByTagName('head')[0].appendChild(v);   What I want to do is reference the script element that loaded the current script so that I can then append my new dynamically loaded script tags into the DOM after it.  &lt;script type="text/javascript" src="scripts.js"&gt;&lt;/script&gt; loaded by scripts.js--&gt;&lt;script type="text/javascript" src="new_script1.js"&gt;&lt;/script&gt; loaded by scripts.js --&gt;&lt;script type="text/javascript" src="new_script2.js"&gt;&lt;/script&gt; I am trying to find examples of maps between topological space which are local homeomorphism but not covering maps. Especially, how twisted has to be such a counterexample : can it be a local diffeomorphism between connected manifolds which is not a covering map ?   I found here() a nice proposition which state that a local homeo from a compact space to a connected Hausdorff space is a covering map.   I am interested in all type of counterexamples, from non-Hausdorff spaces to surfaces, to get a better picture of the differences between covering maps and local homeomorphisms.  Thank you ! Almost every time I turn my XBox on and start up Fallout 4, I am unable to use the "Continue" option because the most recent save is corrupt.  I instead use the "Load" option. Here, I can see that the last save I manually performed is perfectly fine, and load it with no problem. However, there is an additional, corrupt save with the same time stamp immediately after it.  This doesn't happen quite every time, but often enough that I'm surprised when there's no corrupt save waiting for me to delete it.  I've tried a few things to solve this, including exiting to the game's main menu before turning the XBox off, going out to the guide before turning the XBox off, turning it off immediately after saving, and waiting a while after saving.  Why do I get all these corrupt saves? Do others have this problem? How do I fix it? How accurate is the location detection on the iPhone's Find My iPhone app