Why didn't the British Ministry of Magic call on their foreign counterparts to help fight in the war against Voldemort?
Is there any hint of of the first Wizarding War being an international event?
Can “due to” and “because of ” be used interchangeably? Is it fine to use due to in place of because of ? How about the other way around? Are any of these sentences ungrammatical?   He was lost because of the storm. He was lost due to the storm. He lost his way due to the storm. He  lost his way because of the storm. I need to cite the journal "Sankhyā: The Indian Journal of Statistics" in a paper.  I would like to draw the ā character properly (i.e., I'd prefer, if possible, to avoid using some hack, such as \bar or \overline).  Question: How do I properly write ā in LaTeX?  I didn't have luck with  (after several attempts in both in capital and lowercase) nor The Comprehensive LATEX Symbol List (searching the file for "ā" and "india" revealed no hits). All my properties are zero, and my array is zero, even though I have populated them with numbers and objects I studied propositional logic, and everyday I see applications of what I learned on the internet, in mathematical books and miscelaneous resources.        One particular case is sentences in the form $a \rightarrow b$ , that is, material implications. While I fully understand the mathematical logic approach to the study of those kinds of formulas, sometimes I get confused about what someone ( using implication sentences in the ordinary language ) is trying to say.        In ordinary language, I often see affirmations in the form of an implication.  One example would be someone affirming that "the moon is made of cheese" $\rightarrow 2+2=4$. [ Kleene, Mathematical Logic ].      I perfectly understand that if we choose the interpretation that gives the antecedent as false ( and the consequent as true ) we get that the whole implication is also true, but I would like to understand EXACTLY what he is trying to say when he AFFIRMS a sentence in the form of an implication. Is he saying that under the commonly agreed interpretation of that sentence ( antecedent = false, consequent = true ), that implication becomes true?      Another example, totally different, would be someone affirming that $x \in \mathbb{N} \rightarrow x \in \mathbb{N}$ or $x \in \mathbb{Z}_{&lt;0}$. Is he now affirming the same kind of sentence or saying something totally different?      When he affirms that sentence, is he saying that he finds the sentence to be a tautology?   Why didn't he say that?          Then, with these two examples we have an affirmation of the same kind of sentence (implication) meaning completely different things, in one case he affirms to say that under the commonly agreed interpretation of the sentence, it is true. In another case, he affirms to say that there's no interpretation that makes the sentence false.       Am I missing something? There is really that ambiguity in ordinary language, when people are affirming sentences?  Can't I just take some general instance of the affirmation of a sentence in the form $a \rightarrow b$ in ordinary language and know exactly what he's trying to say, regardless of the propositions he chooses the substitute $a$ and $b$ for?       Thanks a bunch. I have something like this:  &lt;div class="content"&gt;     &lt;a href="#"&gt;A&lt;/a&gt; &lt;/div&gt; &lt;div class="content"&gt;     &lt;a href="#"&gt;B&lt;/a&gt; &lt;/div&gt; &lt;div class="content"&gt;     &lt;a href="#"&gt;C&lt;/a&gt; &lt;/div&gt;   When one of these links is clicked, I want to perform the .hide() function on the links that are not clicked. I understand jQuery has the :not selector, but I can't figure out how to use it in this case because it is necessary that I select the links using $(".content a")  I want to do something like  $(".content a").click(function() {     $(".content a:not(this)").hide("slow"); });   but I can't figure out how to use the :not selector properly in this case. Cardinality of equivalence relations in $\mathbb{N}$ I came across this long proof on this site:    But I would like to know whether my direction can work.  Say we want to find the cardinality of all equivalence relations in $\mathbb{N}$. Since it is a subset of all relations in $\mathbb{N}$, I conclude it has a cardinality smaller or equal to $\aleph$. Now, define an injective function from $P(\mathbb{N})$ to the set of equivalence relations by matching each subset of $\mathbb{N}$ with the identity relation (which is an equivalence relation in $\mathbb{N}$.  Therefore the cardinality of all equivalence relations in $\mathbb{N}$ is greater or equal to $\aleph$ and using CSB we get the desired result.  Seems legit? Could an argument with false Premises and a true Conclusion be logically valid? Self-deleted posts and the 3 vote / 60 day rule With regards to  post about  and the part about retaining reputation earned from deleted posts that have a score of 3 or better and were visible on the site for 60 days, does this also apply to self-deleted posts and will it continue to do so? I culled a few of my own answers over the weekend that were less than stellar, and my reputation dropped 1.8k, but the rep is back today after the changes were announced. I thought it would be useful to clarify that this also applies to self-deleted stuff. What does this symbol mean? (looks like a 1 with double vertical line) I'm studying a course on probability and statistics and at some point this symbol comes up without introduction. It looks like the number one, but slightly bigger and with a double vertical line.  First time it comes up is when discussing stochastic/random variables that are neither continuous nor discreet in an example:   And somewhat later in a proof:    Anyone got an idea what this symbol represents?  EDIT: Thanks for the fast answers, I was still editing the question for better (larger) images :) Frea is trying to kill me I've been trying to play the Dragonborn DLC for Skyrim on the PS3. In order to advance the story, I need to talk to Frea and her dad. But every time I go near the village they try and murder me for slaughtering the village back when I was like level 15 (I'm level 43 now).  I've tried yielding but they won't accept it and I don't know how to make them stop, all I want to do is finish the story. Does anybody know how to fix this issue? Inverse images of images, images of inverse images of a set of vectors What can be said about$\ f^{-1}(f(S))$ and$\ S$, where$\ f(S):=\{f(x):x \in S\}$?   I feel as if$\ f^{-1}(f(S))$ will be smaller than or equal in size (number of elements) to$\ S$.  For example, if$\ f(x)=x$, then$\ f(\{-1, 0, 1, 2\})=\{-1, 0, 1, 2\}$and$\ f^{-1}(f\{-1, 0, 1, 2\})=\{-1, 0, 1, 2\}$ (same size).  But if$\ f(x)=x^2$, then$\ f(\{-1, 0, 1, 2\})=\{0, 1, 4\}$ and$\ f^{-1}(f\{0, 1, 4\})=\{0, 1, 2\}$, which is a little bit smaller than$\ S$.   What can be said about$\ f(f^{-1}(U))$ and$\ U$, where$\ f^{-1}(U):=\{x \in X:f(x) \in U\}$?   The same size as each other? Always?? Can you trade Pokemon from 7th gen (Sun/Moon) to 6th gen (XY, ORAS) and back? Title says it all, I don't see confirmation in  and a cursory google search seemed to say assume no and speculate about the pokemon bank. How does the Higgs mechanism work? I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding? How to split strings into text and number? Cards entering the battlefield simultaneously and "Enter the Battlefield" effects I was playing modern with the owner of a shop.  He played a  which he used to bring in 7 lands: 5 basic mountains and 2  cards.  He then claimed that each  triggered 5 times (killing me).  I am doubting this now.    Here is my reason: The two  cards entered at the same time as the other 5 basic lands.  That means when they were on the battlefield and their ability was in effect, the other 5 basic lands were already there too.  That seems too late to trigger a "Enters the Battlefield" effect.  So here is my question.  Am I right or wrong?  If I am wrong, please show me how the enter the battlefield effect can trigger for something that enters the battlefield at the same time as itself.  If I am right, please show me the rules that prove it.  I now have two shop owners that are convinced that this is a legal play.  If it is not legal, I am going to need clear rules citations to convince them.    Side note:  If I am wrong and it is a legal play, then I have a follow up scenario.  Say I have 2  cards and 5 other human cards in my graveyard.  If I play a spell that lets me return all of them to the battlefield at the same time (say ), would the  cards get 6 +1/+1 counters on them?    To me, if the trick that was played on me with  is legal then my  cards should also get the +1/+1 counters. If a set is linearly independent, a finite subset of that set is also linearly independent Is the above statement true? If I have already proven that the set is linearly independent, is it automatically given that the subset is also linearly independent? If so, how would I go about showing that as a proof. In what order should I watch the various Stargate TV Series? I am unfamiliar with the (multiple) Stargate shows and films, other than the movie which I saw a while ago. I want to try watching the series to see if it is something that I like.   What are the non-subjective facts about the series (without spoilers) that I should be aware of when figuring out which series to start with, for example the original airing order of the series, chronological order of the series, frequency of references to a series other than the one that I'm watching, etc. Regular Expression to match valid dates I'm trying to write a regular expression that validates a date.  The regex needs to match the following   M/D/YYYY MM/DD/YYYY Single digit months can start with a leading zero (eg: 03/12/2008) Single digit days can start with a leading zero (eg: 3/02/2008) CANNOT include February 30 or February 31 (eg: 2/31/2008)   So far I have   ^(([1-9]|1[012])[-/.]([1-9]|[12][0-9]|3[01])[-/.](19|20)\d\d)|((1[012]|0[1-9])(3[01]|2\d|1\d|0[1-9])(19|20)\d\d)|((1[012]|0[1-9])[-/.](3[01]|2\d|1\d|0[1-9])[-/.](19|20)\d\d)$   This matches properly EXCEPT it still includes 2/30/2008 &amp; 2/31/2008.  Does anyone have a better suggestion?  Edit: I found  on RegExLib  ^((((0[13578])|([13578])|(1[02]))[\/](([1-9])|([0-2][0-9])|(3[01])))|(((0[469])|([469])|(11))[\/](([1-9])|([0-2][0-9])|(30)))|((2|02)[\/](([1-9])|([0-2][0-9]))))[\/]\d{4}$|^\d{4}$   It matches all valid months that follow the MM/DD/YYYY format.  Thanks everyone for the help. Table with 100 % width and vertical / horizontal alignment I want to draw the following table in LaTeX. In the first column the text should be left aligned. The text in all other cells should be centered. The first problem occurs with D in the first row. If I write a \centering in front of D, I get a LaTeX error. The second problem is, that I want to vertically align the text in all cells but I don't know how. I have found a solution but it doesn't work if the width of the first column is specified.  \documentclass{article} \usepackage{blindtext} \usepackage{tabularx}  \begin{document}   \begin{tabularx}{\textwidth}{|p{4cm}|X|X|X|X|}     \hline                &amp; \centering A &amp; \centering B &amp; \centering C &amp; D\\     \hline     \blindtext &amp; 123 &amp; 123 &amp; 123 &amp; 123\\     \hline   \end{tabularx} \end{document} Summing data from column in the Attribute table I'm working with population data, and I have an issue when it comes to knowing the sum of a population inside the attribute table.  In my attribute table, I'd like to add all the numbers in the red box, i.e. all the numbers together from the column &quot;UN_2015_E&quot;. Is there a way to do so?