From time to time, the reputation notifier in the top bar notifies me of a +1 reputation change, which I am pretty sure is due to an answer having been deleted on which I had cast a downvote. However, it does not show me this, let alone which answer was deleted.  While I am happy about every drop of reputation, this positive effect gets more than compensated by the negative effect that I cannot directly figure out which of my many downvotes is responsible for this and just got alerted for pretty much nothing.  I can also imagine that this is somewhat confusing for users who are not sufficiently familiar with the system yet.  I thus propose to disable notifications of such events or at least include the information, which question the deleted answer belonged to. Note that I am fine with this reputation being calculated into the next “big” event, I just oppose the alert.
Fine, the 's math  did in the old pop-up. That makes sense. But this is just silly. Why do I need to be notified that a post I downvoted got deleted?    (The title links next to the red -1s were removed from the screenshot by me. They're present in the real pop-up.)  So I can break out a bottle of the '82 Rothschild? It's especially pointless because there's  that caused the change.  Please don't display the Rep Signal when the change is only due to someone else's deleted posts.
Limit problem arctg (1 ^ infinty) Can anyone help me with this limit problem without L'Hopital rule and Taylor series? $$\lim_{x\rightarrow\ -\infty}\left(-2\frac{\arctan(x)}{\pi}\right)^x$$ I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty hypersurface, then $X$ and $H$ meet.   Following the hint, I've done the following: By assumption, $X$ is given by $V(I)$ for some homogenous prime ideal $I\subset k[x_0,\dots x_n]=:A$ and $H$ by $V(f)$ for some homogenous polynomial $f\in A$. We wish to prove that there is a homogenous prime ideal $\mathfrak{p}$ (that's not the irrelevant one) containing both $I$ and $f$.  Consider the affine cone $\mathrm{Spec}\ A/I$ of $X$ in $\mathrm{Spec}\ A$. Being homogenous, both $I$ and $f$ are contained in the ideal $(x_0,\dots x_n)$. By Krull's principal ideal theorem, every minimal prime ideal containing $f\mod I$ has codimension one. $X$ having dimension at least one implies that there are homogenous prime prime ideals $\mathfrak{q}\supsetneq \mathfrak{r}\supset I$. This implies that $(x_o,\dots x_n)$ has codimension at least two. Thus there are prime ideals containing $f\mod I$ that are contained in $(x_o,\dots x_n)$. However, I'd need to show that there are homogenous such prime ideals, right? I'd rather get hints than full solutions. Why my U.S. B1 Visa got refused under 214 (b)? I went for B1 U.S. Visa at the U.S. Embassy in Delhi.   Interviewer: *Good Morning*. Me: *Good Morning* Interviewer: *What is your designation?* Me: *I am a Software Engineer.* Interviewer: *What is the name of your company?* Me: *It is XXX (I replied).* Interviewer: *What is the name of your client?* Me: *It is YYY (I replied).* Interviewer: *Have you ever been to U.S. before?* Me: *NO* Interviewer: *Have you ever been abroad before?* Me: *NO*   At this point he rejected my Visa with letter mentioning 214 (b) as the reason. I don't know why he actually rejected it.  But, I have decent 2+ years of experience with my company. And, I was going on a business meeting with the client. I would have come back after 2 weeks.  I don't know if re applying will help. Why can't I paste § into a Minecraft command? Is there a direct download link with a raw data dump of Stack Overflow? (not a torrent) I would like to create a local MySQL copy of Stack Overflow for academic purposes (school project). As far as I know, the database dump of the  database is available only in an XML format that I will have to convert to SQL on my own with some tool.  Most of direct download links I found were broken (404). The only non-torrent source that I have found and that is still alive is  but the latest Stack&nbsp;Overflow dump there is from October 2009, content of which looks like this:    Where could I find a direct download link with the Stack&nbsp;Overflow dump?    Note: I am not able to use torrents due to network policies, yet for the completeness of this question, here's the link that might help someone:    Other related questions / links that haven't helped me:     ~ all links there give 404  ~ from September '09 with another broken link  ~ from about a year ago with a clearbits.net link  ~ also not working anymore I would like to have multiple bibliographies (reference lists) as described in   ().   However, I'd like to use with a single .tex file, which would contain the bibliography database embedded, as in  ...   Now, I want to use letter documentclass, for which the bibliography needs to be defined ()   So what I end up is with this example (code below, compiled with just pdflatex, no bibtex(which I'd like to avoid in this case)):     ... obviously, something works (multibib recognized primary and secondary cites, assigning them number "1" as start) -- however I don't get two, separate primary and secondary list of references; would that be possible in this context? (doesn't have to be with multibib, but I'd like to avoid a separate .bib file and a bibtex call)  EDIT: I'd also like separate cite keys (i.e. rendered as [a1] and [b1]; not yet sure if multibib can do that; edit: no it cant,  says "You can also edit the .bbl files created by BibTEX and add 'a', 'b',. . . to the labels, but your changes will be overwritten by subsequent BibTEX runs." and recommends \cite[a]{key}) - how possible would that be?  &nbsp;  The code is this:   \documentclass{letter}  % Environment thebibliography undefined when using letter: http://www.latex-community.org/forum/viewtopic.php?f=4&amp;t=3359 \makeatletter \setlength \labelsep {.5em} \newcommand\newblock{\hskip   .11em\@plus.33em\@minus.07em} \let\@openbib@code\@empty \newcommand\refname{References} \newcommand\section{\@startsection   {section}{1}{\z@}%   {-3.5ex \@plus -1ex \@minus -.2ex}%   {2.3ex \@plus.2ex}%   {\normalfont\Large\bfseries}} \newenvironment{thebibliography}[1] {\section*{\refname}%   \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}%   \list{\@biblabel{\@arabic\c@enumiv}}%   {\settowidth\labelwidth{\@biblabel{#1}}%     \leftmargin\labelwidth \advance\leftmargin\labelsep \@openbib@code     \usecounter{enumiv}%     \let\p@enumiv\@empty \renewcommand\theenumiv{\@arabic\c@enumiv}}%   \sloppy \clubpenalty4000 \@clubpenalty \clubpenalty   \widowpenalty4000%   \sfcode`\.\@m} {\def\@noitemerr {\@latex@warning{Empty       `thebibliography' environment}}%       \endlist} \makeatother  \usepackage{multibib} \newcites{pri}{Primary sources} \newcites{sec}{Secondary sources}  \begin{document}   \begin{letter}{Addressee} Blah, blah - content...  Primary cite: \citepri{lamport94} ...  Secondary cite: \citesec{lamport94} ...   \begin{thebibliography}{9}  \bibitem{lamport94}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1994.  \bibitem{lamport95}   Leslie Lamport,   \emph{\LaTeX: A Document Preparation System}.   Addison Wesley, Massachusetts,   2nd Edition,   1995.  \end{thebibliography}  \end{letter}   \end{document} I'm an avid book collector, and I was wondering what house has the most bookshelves in Skyrim. I currently only own the Whiterun house, which has 2 bookshelves of 2 shelves each.  Is there a house I could buy that has more bookshelves?  Edit  Since not all bookshelves hold the same number of books, I'm looking for the house that has the most spaces on bookshelves for books, not necessarily the most bookshelves Whenever I play a PC game with the directional keys, I can only press two buttons at a time.  For instance if I am playing a shooter like R-Type, I cannot hold down the fire button while moving diagonally at the same time.  The computer simply ignores the extra button press.  How do I remove this limit so I can shoot while moving diagonally?  This limitation seems to apply for every game.  I am running Windows 7 if it makes any difference.  I noticed the same problem back when I used Windows XP. Real Roots and Differentiation Prove that the equation $x^5 − 1102x^4 − 2015x = 0$ has at least three real roots.  So do I sub in values of negative and positive values of $x$ to show that there are at least three real roots? The method to do this question is not by finding the factors of $x$ right? Because it will be too tedious so I want to ask whats the other solution to prove this? Help appreciated. Thank you very much. Unable to mount Windows (NTFS) filesystem due to hibernation Homework - set theory infinite union A question from my homework I'm having trouble understanding. We are given:  $A(1) = \{\varnothing\}$, $A(n+1) = A(n)\cup (A(n)\times A(n))$  $A=A(1)\cup A(2)\cup A(3)\cup \cdots \cup A(n)\cup A(n+1) \cup \cdots$ to infinity  The questions are:  1) show that $A\times A \subseteq A$  2) Is $A \times A = A$?  Thank you for your help.  I've tried writing $A(2)$ but it gets really complicated and I'm having trouble understanding what the sets are. Let alone solve the question. Are there any best practices for choosing the title of web pages? There are a lot of resources online oriented toward SEO, but not toward users.  My impression is that most sites have something similar to Product - Page. But there are cases when switching this around is more useful. For example, if mail clients displayed the title like this:  Inbox (3) - Gmail  Instead of:  Gmail - Inbox (3)  You would be able to see the message count, even if the title was cut off. (I'm pretty sure Gmail used to do this).  I assume the title is mostly ignored by users except when:   using boorkmarks finding the right tab in the browser   What are the considerations for users when choosing a web page title? Are there different considerations for the home page, pages behind a login, etc? I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } Borel set preserved by continuous map Let $f:\mathbb{R}^m\rightarrow\mathbb{R}^n$ be a continuous map. Show that if $A$ is a Borel subset of $\mathbb{R}^n$, then $f^{-1}(A)$ is a Borel subset of $\mathbb{R}^m$.   I know that for $A$ open subset of $\mathbb{R}^n$, then $f^{-1}(A)$ is open. Likewise for closed. A Borel subset is a countable unions/intersections of these sets, done repeatedly. From those facts, combined with $f^{-1}(A\cup B)=f^{-1}(A)\cup f^{-1}(B)$ and $f^{-1}(A\cap B)=f^{-1}(A)\cap f^{-1}(B)$, the statement should be intuitively true.  But to do it rigorously, I want to write $A$ as open and closed sets. But since the countable union/intersection can be done repeatedly, I don't know how I can write it that way. How to host my existing website with Google Drive Google has given me 15GB of storage. Can I host my own website having my own domain? How to toggle Scroll Lock in Excel 2010 without a Scroll Lock key in the keyboard I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? We want to encrypt / encode URL parameters on our pages. I tried to encrypt a parameter using  with AES algorithm as explained in the   %%[SET @encData=EncryptSymmetric("test", "AES", @null, "1111", @null, "0000000000000000", @null, "00000000000000000000000000000000") ]%% AES: %%=v(@encData)=%%   The result of this function is      AT1r0irnzM+Ax1j8zN+zAw==   Then I tried to decrypt the value using an , but I always received an error message.  I suppose there is a difference between AES algorithm in Marketing Cloud and AES used in the online tool. Indeed if I encrypt the same word with an online tool (128-bit), I received this result      l4Yo3sFofFD1EMmtoh397w==   Do you have any deep information regarding this function? What could be the difference? Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism? Let $V$ and $W$ be vector spaces (say over the reals). There is a linear injection $V^* \otimes W^* \to (V \otimes W)^*$ which sends $\sum_i f_i \otimes g_i \in V^* \otimes W^*$ to the unique functional in $(V \otimes W)^*$ sending $v \otimes w \mapsto \sum_i f_i(v) \cdot g_i(w)$ for all $(v,w) \in V \times W$. In the finite dimensional case it is easy to see this is an isomorphism by comparing dimensions on both sides. I'm aware that this is not an isomorphism in the infinite-dimensional case (see Relation with the dual space in the  on tensor products) but I must admit that I'm not sure why. Cardinal arithmetic does not seem help here and, even if it did, I would be much happier to see an explicit example of a functional in $(V \otimes W)^*$ outside the range of this map. I'm having trouble cooking one up myself.  Added: Let me elaborate on my comment about cardinal arithmetic. Suppose that $X$ and $Y$ are infinite dimensional vector spaces over a field $k$. I'm confident that $\dim (X \otimes Y) = \dim X \cdot \dim Y$ holds. It is clear that $|X^*| = |k|^{\dim X}$ since we may identify a functional on $X$ with a function from a basis for $X$ to $k$. Also I think I've convinced myself that if $\dim X \geq |k|$ then in fact $|X| = \dim X$ ie. the cardinality and dimension of a vector space agree when the dimension is larger than the cardinality of the ground field. Consequently, assuming say that $|k| \leq \dim X \leq \dim Y$ it seems we have $$ \dim(X \otimes Y)^* = |k|^{ \dim X \cdot \dim Y} = |k|^{ \dim Y} = \dim Y^* = \dim X^* \cdot \dim Y^* = \dim (X^* \otimes Y^*)$$  which implies that in fact $(X \otimes Y)^*$ and $X^* \otimes Y^*$ are isomorphic but, rather frustratingly, the obvious map does not do the job. Did I make a mistake here? If not, is it generally true (ie without making assumptions about $|k|$) that there exists some isomorphism $(X \otimes Y)^* \to X^* \otimes Y^*$? Who did that to the priest's dog? In John Michael McDonagh's wonderful philosophical black comedy , a good priest receives a death threat during a confessional giving him a week to sort out his affairs.   During the course of the week there are a lot of encounters between the priest and his parishioners, many acting as red herrings to distract the audience form the identity of the potential killer. Several threatening acts also take place: the church is burned and the priest's dog is killed.   But in the final encounter between the priest and the mystery antagonist (I'm not saying who to avoid spoilers) the antagonist admits burning the church but claims not to have killed the priest's dog.  Are they lying? Or is there a good reason that someone else might have killed the dog? How do you concatenate matrices? And how do you make block matrices?