I wonder which sentence is the right one.     What are you going to do after school?   vs     What are you going to do after the school?   To me, I feel like "after the school" is the right one, but I might saw "after school" on the TV before.
Jamaica Inn episode 5 from BBC learning English drama section:  The dialogue says:     Mary: My aunt is in bed.   She doesn't say -      My aunt is in the bed.   That section is for teaching English.  Are they using incorrect English?
Prove or disprove: if $\sum\limits_{n=0}^∞a_n$ converges and $\lim\limits_{n\to\infty}b_n =0$, then $\sum\limits_{n=0}^{\infty}a_n b_n$ converges. Intersection of open affines can be covered by open sets distinguished in *both*affines Suppose $X$ is an arbitrary scheme and $U \cong \operatorname{Spec} A$ and $V \cong \operatorname{Spec} B$ are affine upon subsets of $X$.  It's not true in general that $U \cap V$ is affine, so if we want to prove basic results about general schemes (e.g. the stuff in section II.3 of Hartshorne), we need some technical means of understanding what goes on on the intersections of open affines.  I've heard that this can be done by covering $U \cap V$ with open sets which are distinguished in both $U$ and $V$, i.e. sets $W \subseteq U \cap V$ with $W \cong \operatorname{Spec} A_f \cong \operatorname{Spec} B_g$ for some $f \in A$ and $g \in B$.  I'm having trouble actually proving this.    So, questions:   Is this actually true? If so, how are these sets constructed? Remove sudo privileges from a user (without deleting the user) $\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$ Could you explain how to find this limit?  $\lim_{n \rightarrow \infty} \sum^n_{k=1} \frac{1}{k+n}$ How to eliminate Cycles artifacts with many overlapping volumes? I have encountered an issue with Cycles Volumetrics in a recent scene. I am using Blender 2.72, and both CPU and GPU render options. In both I get a solid black artifact when I have two volumes overlapping, as in this campfire smoke test:    I have a solid cube, with a volume scatter and volume absorption material, duplicated by a particle system. As you can see, when the particles get higher up and farther apart, and are no longer overlapping, the artifacts disappear. Why rationalize the denominator? In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$.  says that "there is a bias against roots in the denominator of a fraction". But such fractions are well-defined and I'm failing to see anything wrong with $\frac{1}{\sqrt{2}}$ - in fact, IMO it is simpler than $\frac{\sqrt{2}}{2}$ because 1 is simpler than 2 (or similarly, because the former can trivially be rewritten without a fraction).  So why does this bias against roots in the denominator exist and what is its justification? The only reason I can think of is that the bias is a relic of a time before the reals were understood well enough for mathematicians to be comfortable dividing by irrationals, but I have been unable to find a source to corroborate or contradict this guess. Solution to German Tank Problem Is there a formal mathematical proof that the solution to the  is a function of only the parameters k (number of observed samples) and m (maximum value among observed samples)? In other words, can one prove that the solution is independent of the other sample values besides the maximum value? How to hide the [@] in a Minecraft command block How can I add metadata to NTFS files/folders? I want to tag different file types (i.e. .pdf, .epub, .iso, .bin, folders,..) using the same descriptive fields. For example i would like a metadata field "type" which would be "eBook" on pdf- and epub-files, "CD-Image" on iso- and bin-files.  I read about Alternate Data Streams (ADS) to make this possible. Does anyone know a good program for Windows 7 to tag different files and search for them? It is important for me, that the metadata is NOT stored in a separate database. I move the files a lot and need to stay flexible (ADSs 'stick' to the files).  Any ideas? We work heavily with serialization and having to specify Serializable tag on every object we use is kind of a burden. Especially when it's a 3rd-party class that we can't really change.  The question is: since Serializable is an empty interface and Java provides robust serialization once you add  implements Serializable - why didn't they make everything serializable and that's it?    What am I missing? Yesterday, I've listened to a song called "Fear not this night". I find the syntax unusual (as a foreigner, I have never encountered it). Is it the same meaning as "Don't fear this night" ? What's the slight difference between these 2 ?  Thank you for your time. Project Euler Question 14 (Collatz Problem) Show  $$\int_0^\infty \frac{\ln(x)}{e^x} = -\gamma$$ (gamma is Euler-Mascheroni constant).  Can anyone please prove this result?  Also  $$ \int_0^\infty \frac{\left( \ln(x) \right)^2}{e^x}\mathrm dx. $$ Sci-Fi book female fighter pilot All I remember about the book is that the protagonist was a human female fighter pilot, she has short hair, not sure if it was blond or auburn and she was involved in making peace with the alien race.  The alien race was invading Earth, but because of her they stopped, surrendered and because of her helped Earth improve its technology. I remember that she melded with something and was starting to sort of think like them and lose a bit of her humanity.  It was set in the not too distant future. I believe I read it in the 90s. Drush from GitHub stopped working How can we unlock an iPhone backup file if we don't know the password? Notes:  Answers will occasionally be moved to the  when there are too many of them. When using them to report bugs, keep an eye on the post.    This site, Meta Stack Exchange, is usually used as a &quot;test bed&quot; for pending changes happening to the way text is rendered on all network sites. Changes to text rendering that are going to be rolled out to the network are usually deployed here first to test them out and fix any potential glitches. Currently, there are no such changes pending, but if there were, keep in mind that text posted here may render differently from the other sites until the changes roll out to them as well.    As per Jeff's suggestion in : You can use this question as a formatting sandbox. You can:  edit  itself ( questions such as this one require only 100 reputation to edit instead of 2,000) post answers to this question (This question might be , requiring earning 10 reputation on this site to answer) post comments to this question or its answers test suspected bugs with the editor or the rendering post ponies (only when mods are asleep)   Beware that since the  in December 2010, and  added in March 2011, no syntax highlighting is applied unless the question's tags or an inline hint enable it. So, to test highlighting here in the sandbox:  , you can use GitHub-flavor fenced code blocks in your posts, specifying the language after the opening fence: ```html While not hinted otherwise: &lt;html&gt;&lt;/html&gt; source &lt;b&gt;goes&lt;/b&gt; &quot;here&quot;. ```  ```js var a = 3; while (not (a &gt; 0)) {     alert(&quot;JavaScript code &lt;b&gt;goes&lt;/b&gt; here.&quot;); } ```   Or:  Create code blocks in any way (using the fence notation above, the four-space indent form, or using HTML &lt;pre&gt;&lt;code&gt; tags).  Save your post.  Use your browser's developer tools to edit the resulting HTML. To open developer tools, press F12, or ⌥⌘ I on Mac.  Find the &lt;pre&gt; element and add the attribute class=&quot;prettyprint&quot;, or change it into one of the valid syntax hints linked above, like class=&quot;lang-vb prettyprint&quot;.  Run the following in the location bar: javascript:prettyPrint(); or prettyPrint() in the console.     Answers that are considered annoying or obnoxious, or that cause breakage for users, will be deleted. This is . Open Finder window from current Terminal location? If I am in a specific path in a Terminal window, how can I open that same window in a new Finder window?   Note: This is the opposite of . Suffixes indicating people and language of country vary by country:  _an: American, German, Italian, Belgian, Australian, Russian, Ukrainian, Korean,  Mexican, Brazilian, Chilean, Argentinean, Indonesian, Malaysian, Iranian, Egyptian, Somalian, Palestinian  _sh: English, British, Polish, Danish, Swedish, Turkish,    _ch: French, Dutch  _ese: Chinese, Taiwanese, Japanese, Vietnamese, Portuguese  _no: Filipino, Latino  _i: Israeli  _: Thai  Among the above, _an seems to outnumber other suffixes.  Are there any simple rule to govern appropriation of suffix turning a country name into adjective, indicating people and language of countries in the world in terms of say, region, race, or cultural background? Or is it just discretional? Mark a comment as the answer to a question