The use of was and were with singular nouns
When should I use the subjunctive mood?
Based on the following interchange between Harry and Dumbledore in the pivotal &quot;King's Cross&quot; chapter of Deathly Hallows, I was wondering when exactly Dumbledore put together that Harry would have to die in order to bring about Voldemort's ultimate demise:  &quot;And you knew this? You knew--all along?&quot; &quot;I guessed. But my guesses have usually been good,&quot; said Dumbledore (Deathly Hallows, 599, hardcover).  The conversation that spurred Harry's question includes material dating back to Halloween '81, but also specifically mentions the events of the graveyard from GoF. So, &quot;knowing all along&quot; could refer to everything (i.e., Harry must die, Voldemort ignorantly tethered him to life, etc.) or just that Voldemort tethered him to life. Other important information pertaining to this question can be found in OOTP, when Dumbledore confirms (if he didn't already know) that Harry contains part of Voldemort's soul. He uses the silver instrument to find out that Harry is just like Nagini, having the ability to share mind and soul with Voldemort. He also says the following:  &quot;I guessed, nearly fifteen years ago,&quot; said Dumbledore, &quot;when I saw the scar upon your forehead, what it might mean. I guessed that it might be the sign of a connection forged between you and Voldemort&quot; (Order of the Phoenix, 826-827, hardcover).  While confirming that he guessed that Harry might share a connection with Voldemort from the very beginning, Dumbledore does not confirm with this statement that he knew Harry would ultimately have to give up his life. In Philosopher's Stone, when Dumbledore drops off Harry on the Dursley's doorstep, we know he is not entirely truthful with McGonagall.  McGonagall asks: &quot;How in the name of heaven did Harry survive?&quot; &quot;We can only guess,&quot; said Dumbledore (Philosopher's Stone, 12, hardcover).  Of course, this was a lie. Dumbledore already knew how Harry survived, otherwise he wouldn't be delivering Harry to Lily's sister to extend the blood sacrifice. By proxy, he also knows that Voldemort will return b/c of Horcruxes, otherwise he wouldn't be so worried about Harry. Finally, when asked in the same scene if he could remove the scar, Dumbledore says:  &quot;Even if I could, I wouldn't. Scars can come in handy&quot; (Philosopher's Stone, 15, hardcover).  So, did Dumbledore know at this very moment that Harry would have to die? Did he at least guess it to be true during this scene? We know he gains perfect confirmation in OOTP, but did he know it &quot;all along,&quot; as a particular reading of the King's Cross interchange in DH would have us believe? Irreducible polynomial which is reducible modulo every prime How to show that $x^4+1$ is irreducible in $\mathbb Z[x]$ but it is reducible modulo every prime $p$?   For example I know that $x^4+1=(x+1)^4\bmod 2$. Also $\bmod 3$ we have that $0,1,2$ are not solutions of $x^4+1=0$ then if it is reducible the factors are of degree $2$. This gives that $x^4+1=(x^2+ax+b)(x^2+cx+d)$ and solving this system of equations $\bmod 3$  gives that $x^4+1=(x^2+x+2) (x^2+2x+2) \pmod 3$. But is there a simpler method to factor $x^4+1$ modulo a prime $p$? Borel-Cantelli-related exercise: Show that $\sum_{n=1}^{\infty} p_n < 1 \implies \prod_{n=1}^{\infty} (1-p_n) \geq 1- S$. This is supposed to be related to the  (my justification for the independence tag). In Williams' Probability with Martingales, 2BCL is proven and then the following is given as an exercise:  Prove $S \doteq \sum_{n=1}^\infty p_n &lt; \infty \implies \prod_{n=1}^\infty (1-p_n) &gt; 0$ assuming $0 \leq p_n &lt; 1$. Hint: Show that $S &lt; 1 \implies \prod_{n=1}^\infty (1-p_n) \geq 1 - S$.   Proving the hint: I tried to find $\{a_n\}$ s.t. $$\prod_{n=1}^\infty (1-p_n) \geq \prod_{n=1}^\infty e^{a_n} = e^{\sum_{n=1}^\infty a_n} \geq 1 - \sum_{n=1}^\infty a_n \geq 1 - S &gt; 0$$ That is, find $\{a_n\}$ s.t.: 1a. $1 - p_n \geq e^{a_n}$ 1b. $a_n \leq p_n$ I thought of $a_n = \ln(1-p_n)$ (a reason why $p_n &lt; 1$, I guess) Is that right? Edit: Actually, assuming my proof is right, is $S &lt; 1$ used in the proof? If so, where?  From Williams book: Search for a string and print everything before and after within a range I have this file:  sometext1{ string1 }  sometext2{ string2 string3 }  sometext3{ string4 string5 string6 }   I want to search this file for a specific string and print everything before this string up to the opening { and everything after this string up to the closing }. I tried to achieve this with sed but if I try to print everything in the range /{/,/string2/ for example sed prints this:  sometext1{ string1 }  sometext2{ string2 sometext3{ string4 string5 string6 }   If I search for the string "string2" I need the output to be:   sometext2{ string2 string3 }   Thanks. Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant? Let $f\colon[0,1]\to\mathbb{R}$ be continuous such that $f(x)\in\mathbb{Q}$ for any $x\in[0,1]$. Intuitively I feel that $f$ is constant, since $\mathbb{Q}$ is dense in $\mathbb{R}$.  How can I formally write this down? I'm no expert in darkroom photography, but it seems a little odd that there is a type of light that doesn't affect film or developing paper etc. The only way that I could think to explain it is:   The low frequency red photons don't have enough energy to raise electron states in the film/paper, or Magic   either way, I'm curious to know how this handy tool is, as per title, safe. I've seen many boads with weird zig-zag shaped tracks just like the one below. Why are they designed like that? Does the mass of a battery change when charged/discharged? If so, how much? Is it possible to detect it, or is it beyond any measurement?  I'd say there are two possible scenarios (depending on the battery type) and both seem interesting:   The battery reacts chemically with its environment. The battery doesn't exchange any matter with its environment except electrons. I suppose there should be some difference at least due to the principle of energy-matter equivalence, but the difference is most likely immeasurable. Can I install Microsoft Office? If so, how? I want to know how to install Microsoft Office (specifically, Microsoft Office 2010) in Ubuntu?   I am a die hard fan of MS Office and I want to know if there is a way I can use it in Ubuntu. One word for someone who always does what he loves I am looking for one word to describe someone who always does what he loves.   Loving means enjoying something very much, free-spirited means not restrained by convention. Is there a hybrid word?   I mean a word that describes someone who is independent and always does what he loves. Please also try to not make the word too esoteric. Also, the word needs to be positive.  How will it be used?  I am submitting an application for college, and they require me to supply a word to describe myself. I have always done what I love. So, I require a word to describe someone who loves what they want. There is no sentence, in particular, just a prompt asking me to describe myself in one word. What governor limits impact Apex Describe methods? Is it legal/well-defined C++ to call a non-static method that doesn't access members through a null pointer? Call native javascript function that has been "erased" by the web page Greek Text (babel) and English Code Text (listings): Problem I use the babel package in order to write in greek with font "kerkis".  I want to add code in english ("courier new" font) to my latex document but I get some difficulties.  Can anybody help me, please. Thank you in advance.  \documentclass[12pt]{article} \usepackage[english,greek]{babel} \usepackage[utf8x]{inputenc} \usepackage{graphicx} \usepackage{fancybox} \usepackage{verbatim} \usepackage{courier} \usepackage{kerkis} \usepackage{float} \usepackage{geometry} \usepackage{fancyhdr} \usepackage{titlesec} \usepackage{tocloft} \usepackage{hyperref} \usepackage{afterpage} \usepackage{color}    \usepackage{listings}  \renewcommand{\lstlistingname}{Κώδικας}  \lstset{  %matlab   backgroundcolor=\color{white},     basicstyle=\normalsize,    % COURIER NEW?        commentstyle=\color{green},    % comment style   escapeinside={\%*}{*)},           extendedchars=true,               frame=single,                              keywordstyle=\color{blue},       % keyword style   numbers=left,                     numbersep=5pt,                     numberstyle=\normalsize\color{black},    rulecolor=\color{black},           stepnumber=1,                      stringstyle=\color{magenta},     % string style }   \begin{document}  \selectlanguage{greek} Ελληνικά: \textlatin{this word means greek}  \selectlanguage{english} Now I write in english  \selectlanguage{greek} Ελληνικά  %\selectlanguage{english}???  \begin{lstlisting}[caption = \textlatin{example1.m}] { % Entropy E = 0; for i = 1:J     if p(i) ~= 0         E = E + p(i)*log2(1/p(i));     end end } \end{lstlisting}  \end{document} Why does demand for stock rise when a company appears to have high future value? So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance? youtube-dl unable to download audio how to resolve that issue? When will SO stop wasting real estate of my screen by having static width layout?  EDIT  It would be very interesting to hear how does Joel, being UI specialist, feel about this. JoelOnSoftware site has fluid layout... How does the Ranger's Extra Attack feature work with Two-Weapon Fighting? I think I know the answer to this one but I'm double checking.  At the 5th level the Ranger gets Extra Attack, which lets them attack a second time during the Attack action. If they are fighting with 2 weapons, the second weapon normally uses their bonus action.  Does this mean when using the Extra Attack and using two weapons, a ranger can attack twice during the Attack action, and still make 1 extra attack as a bonus action, for a total of 3 attacks? What iron-clad reason did Dumbledore have for believing Snape was on his side I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,­id:"minecraft:diamond_sword"}]­}   but I can't get them together. The block should only look for an item in the active slot.