Why didn't the British Ministry of Magic call on their foreign counterparts to help fight in the war against Voldemort? I am just curious. It was a Huge, destructive and a famous war.  Ministry of Magic could have helped them, but why did it not help?  Please help.
Is there any hint of of the first Wizarding War being an international event? Is there any hint that the MoM or anywhere else got support in combating voldemort the first time around? Or is everything completely UK-centric?  I can't remember anyone in the second war being specifically sent from europe to help, even though we see international wizards in book 4. But I don't think all the events of the first war are covered in the books.  So are other bodies like the MoM involved in the first war, or was it isolated in the UK?
Shape of the universe? What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand equally everywhere in all directions. But they also raise some questions, like if you are on the surface of a balloon and travel in 1 direction, you will eventually return to your starting point, is it possible our universe have this feature?  If it has, or had, would this be a symmetry of sorts ($\psi(x)=\psi(x+R)$), and as such have a conserved quantity associated with it (by Noether)? Assuming "small curled up dimensions" wouldn't these dimensions have this type of symmetry, what are the associated conserved quantities? Is it known exactly what the geometrical shape of the universe is? (on a large scale) (I am not talking about only the observable universe). How does one define the "size" of a dimension, is this scale only applicable to curled up ones? Is it possible to describe to a layman the shape of the universe without resorting to inept analogies? Triangle Inequality of the Cartesian product with Max function Let $(X,d)$ be a metric space.  Define $$d'((x,y),(z,w))=max\{d(x,z),d(y,w)\}.$$   I'm trying to prove the triangle inequality for this, but really don't have a clue how.  Any tips or suggestions would be greatly appreciated! Mount USB drive with write permissions for everyone or specific user We know $$i^2=-1 $$then why does this happen? $$ i^2 = \sqrt{-1}\times\sqrt{-1} $$ $$ =\sqrt{-1\times-1} $$ $$ =\sqrt{1} $$ $$ = 1 $$  EDIT: I see this has been dealt with before but at least with  I'm not making the fundamental mistake of assuming an incorrect definition of $i^2$. "Being" or "to be"? Which is better structured?     "She loves to be herself instead of showing off"    or     "She loves being herself instead of showing off"   or     "She loves being and not appearing" How do I calculate the date six months from the current date using the datetime Python module? Exclude lstinputlisting I want to save paper when I print my LaTeX file. That's why I want to hide all my code, inserted wtih lstinputlisting{}  I already know how to exclude tables and images or math but the lstinputlisting{} is a problem.   Hope someone can help me  \usepackage{comment} \excludecomment{figure} \let\endfigure\relax \excludecomment{table} \let\endtable\relax \excludecomment{align*} \let\endalign\relax \excludecomment{lstlisting} \let\endlstlisting\relax   edit: added lstlisting Why aren't all the badges shown on the track menu? I like using the 'Track Badges' menu on my profile a lot (I know what you're going to say, I just have a knack for these things), but I keep noticing something a bit unusual.  Many of the Badges featured on the actual list do not get featured on this menu. For example, I've been hoping to be able to track progress for the Pundit badge (ten comments with score of five or more), but it doesn't show up in the menu.  Why not? Difference between float and decimal data type Cannot install vim I am running Ubuntu 11.10, as Xubuntu, in an AMD 64 pc, configured as dual boot with Windows 7.  I tried installing vim with this:  sudo apt-get install vim   I got this error message:  The following packages have unmet dependencies:  vim : Depends: vim-common (= 2:7.3.154+hg~74503f6ee649-2ubuntu2) but 2:7.3.154+hg~74503f6ee649-2ubuntu3 is to be installed E: Unable to correct problems, you have held broken packages.   I only have a very faint idea of what the problem is, and none whatsoever on how to correct this. Hope you guys can help. Why are so many different types of objects white, yet appear gray when they are wet? There are many things with different textures that appear white – salt, beer foam, paper, shaving cream, snow, talcum powder, white paint, etc. The most common answer is all of the frequencies must be reflected in order for us to perceive white, which I already know. There must be more underlining details why such a huge variety of things are white. Furthermore, if you wet paper, snow or talcum powder, they appear off-white or gray. Why is this? Is it a problem if a UK visa was issued but not used? Last year, my wife and I were issused 6-month visieor visas for the UK. She did not travel with me and, therefore, didn't use her visa. I am currently applying for a visitor visa for my daughter and myself.  Will the fact that my didn't use her visa have any negative affect on our new application? Where's the BIOS on an Intel Mac? In "Tasksel" how do I select a package? I found a video on YouTube that shows someone using the command tasksel from the server's boot menu after a fresh install of Ubuntu Server. Simple enough it looked like, but when I go to the options I want to choose for installation it has no information on how to select them, and when I click Enter on one of them it takes me back to the command prompt.  So how do I make a selection of the items listed under tasksel?  I have tried Shift++ to add, but no luck. Anyone know?  I want to install Ubuntu Desktop, as Ubuntu GNOME GUI is not an option in the listing for Ubuntu 17.10 Server. Why do all the planets of the solar system orbit in roughly the same 2D plane? Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the orbits distributed all around the sun, in 3D. Has an object made by man (a probe) ever left the Solar System? Closest points on two line segments I am looking for a general formulation to find the closest points on two line segments. What I was thinking about is to define our lines as:  $$ P1 + s  (P2-P1)$$  $$ Q1 + t  (Q2-Q1)$$  Where $P1 , P2, Q1$ and $Q2$ are the beginning and the end points on each segment.  Now we should go through an optimization problem as: $\min f(s,t)$ such that $0&lt;s&lt;1$ and $0&lt;t&lt;1$.  Where $f(s,t)$ is the point-to-point distance function.  Is there any straight forward solution? Proof that every finite dimensional normed vector space is complete Can you read my proof and tell me if it's correct? Thanks.  Let $V$ be a vector space over a complete topological field say $\mathbb R$ (or $\mathbb C$) with $\dim(V) = n$, base $e_i$ and norm $\|\cdot\|$. Let $v_k$ be a Cauchy sequence w.r.t. $\|\cdot\|$. Since any two norms on a finite dimensional space are equivalent, $\|\cdot\|$ is equivalent to the $l^1$-norm $\|\cdot\|_1$ which means that for some constant $C$, $\varepsilon &gt; 0$, $k,j$ large enough, $$ \varepsilon &gt; \|v_j - v_k\| \geq C \|v_j - v_k\|_1 e_i= C \sum_{i=1}^n |v_{ji} - v_{ki}| \geq |v_{ji} - v_{ki}|$$ for each $1 \leq i \leq n$. Hence $v_{ki}$ is a Cauchy sequence in $\mathbb R$ (or $\mathbb C$) for each $i$. $\mathbb R$ (or $\mathbb C$) is complete hence $v_i = \lim_{k \to \infty} v_{ki} $ is in $\mathbb R$ (or $\Bbb C$) for each $i$. Let $v = (v_1, \dots , v_n) = \sum_i v_i e_i$. Then $v$ is in $V$ and $\|v_k - v\| \to 0$:  Let $\varepsilon &gt; 0$. Then $$ \|v_k - v\| \leq C \|v_k - v\|_1 = C \sum_{i=1}^n |v_{ki} - v_i| \leq C^{'}n \varepsilon$$  for $k$ large enough. Proof of greatest integer theorem: floor function is well-defined I have to prove that  $$\forall x \in \mathbb{R},\exists !\,n \in \mathbb{Z} \text{ s.t. }n \leq x &lt; n+1\;.$$  where $\exists !\,n $ means there exists a unique (exactly one) $n$. I'm done with proving that there are at least one integers for the solution. I couldn't prove the &quot;uniqueness&quot; of the solution, and so I looked up the internet, and here's what I found:  Let $\hspace{2mm}n,m \in \mathbb{Z} \text{ s.t. }n \leq x &lt; n+1$ and $m \leq x &lt; m+1$. Since $n \leq x \text{ and } -(m+1) &lt; -x$, by adding both, $n + (-m-1) &lt; (x-x) = 0$. And (some steps here) likewise, $(x-x) &lt; n+m+1$.  Now, can I add up inequalities like that, even when the book is about real analysis (and in which assumptions are supposed to be really minimal)? Or should I also prove those addition of inequalities? Thank you :D Two different expansions of $\frac{z}{1-z}$ This is exercise 21 of Chapter 1 from Stein and Shakarchi's Complex Analysis.  Show that for $|z|&lt;1$ one has $$\frac{z}{1-z^2}+\frac{z^2}{1-z^4}+\cdots +\frac{z^{2^n}}{1-z^{2^{n+1}}}+\cdots =\frac{z}{1-z}$$and   $$\frac{z}{1+z}+\frac{2z^2}{1+z^2}+\cdots \frac{2^k z^{2^k}}{1+z^{2^k}}+\cdots =\frac{z}{1-z}.$$  Justify any change in the order of summation.   [Hint: Use the dyadic expansion of an integer and the fact that $2^{k+1}-1=1+2+2^2+\cdots +2^k$.]  I don't really know how to work this through. I know that $\frac{z}{1-z}=\sum_{n=1}^\infty z^n$ and each $n$ can be represented as a dyadic expansion, but I don't know how to progress from here. Any hints solutions or suggestions would be appreciated. biblatex: Handling secondary ("quoted in") citations This question and the answer became part of a package:      How can I qoute secondary quotes which I’ve taken form another book.  Example  Jon Doe writes a book an cites Fred Bloggs in it. Now I read the book of Doe an want to cite his cite of Bloggs. So my bibliography entry must look like     Bloggs, Fred: A nice old book, 1850, p. 35. Quoted in Doe, John: A bad new Book, 2011, p. 67.   Doe’s book should not be listed separately in the bibliography.  I know that there’s a bibstring quotedin containing “quoted in” (p. 159 of biblatex’s manual) but I don’t know if theres a (predefined) way to use it …  Update  It seems that there’s no predefined way, so I decided to use userc for crossreferences like this. This works for the bibliography but not for cite commands. At the moment I create the “in text cite” manually.  It would be great to have a macro like  \QIautocite[&lt;prenote a&gt;][&lt;postnote a&gt;]{&lt;author a&gt;}[&lt;prenote b&gt;][&lt;postnote b&gt;]{&lt;author b&gt;}   that expands to the above given example.  That’s my new code, which gives the right results for bibliography and “in text cite” but the latter not automatically …  \RequirePackage{filecontents} \begin{filecontents}{\jobname.bib} @BOOKLET{autora,   title = {A nice old book},   userc={autorb},   author = {Fred Bloggs},   year = {1850}, } @BOOKLET{autorb,   title = {A bad new book},   author = {Jon Doe},   year = {2011}, } \end{filecontents}  \documentclass[ngerman]{scrartcl}  \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc}  \usepackage{babel,csquotes,blindtext}  \usepackage[%     bibstyle=authortitle,     citestyle=verbose-ibid, ]{biblatex} \addbibresource{\jobname.bib}  \NewBibliographyString{bibcitedas} \DefineBibliographyStrings{german}{%   bibcitedas = {{zitiert als}{zit. als}}, }  % Put the 'quoted in text' behind the bibentry. \renewbibmacro*{finentry}{%   \ifbibliography{%     \iffieldundef{userc}{}{%       \newunit\bibstring{quotedin}\addspace\fullcite{\thefield{userc}}     }   }{}%   \finentry% }  \begin{document} \blindtext \begin{quotation}     \blindtext\footnote{\cite[36]{autora}. Zit. nach \cite[89]{autorb}} \end{quotation} \blindtext\footnote{\cite[36]{autora}. Zit. nach \cite[89]{autorb}}  \printbibliography \end{document}   Example 2  In addition to my comment (Hi @Audrey. This works fine :-) but theres a little thing …) on Audrey’s answer:  If I use the quotecite command like this  \quotecite[1]{reese}[5]{weinberg} \quotecite[1]{reese}[5]{weinberg} \pagebreak \quotecite[1]{reese}[5]{weinberg} \quotecite[1]{reese}[5]{weinberg}   the footnotes should look like       1 Reese [full cite], p. 1. Zit. nach Weinberg [full cite], p. 65   2 Ebd.   ———— page break ————   3 Rese [short cite], p 1. Zit nach Weinberg [short cite], p. 65   4 Ebd.   Everything works like expected except footnote 3 which is     3 Rese [short cite], p 1. Zit nach Weinberg [full cite], p. 65     at the moment  Update 2  Since it seems not possible to react to autocite I created a new plain command with  \DeclareMultiCiteCommand{\quoteciteplain}[\cbx@qcwrapperplain]{\cbx@quotecite}{\cbx@qcdelim}  \newrobustcmd{\cbx@qcwrapperplain}[1]{%   \global\toggletrue{cbx@isquote}%   #1%   \global\togglefalse{cbx@isquote}%   \global\togglefalse{cbx@iflastibid}%   \global\togglefalse{cbx@ifquoteepost}%   \global\togglefalse{cbx@ifquoterpost}}