Book where technology is a banned form of magic
Book about mages who can harvest magical energy from the environment
Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! How to decide if an effect is magical for Magic Resistance? Some creatures have Magic Resistance:     The [...] has advantage on saving throws against spells and other magical effects.   We know from  that this works against Turn Undead, but does it work against Stunning Strike, Death Strike, Fey Presence, etc? How do we decide? The no. of all possible matrices of order $3\times 3$ with each entry $0$ and $1$ and $ -1$. How do i prove that continuous linear transformation between normed spaces is bounded? Let $(V,||\cdot||_V),(W,||\cdot||_W)$ be normed spaces over $\mathbb{C}$.  Let $T:V\rightarrow W$ be a linear transformation.  Assume $T$ is continuous.  Then, how do i prove that $\exists c&gt;0$ such that $\forall v\in V, ||Tv||_W&lt;c||v||_V$? How to enable/disable a specific graphic card? Deduction of $\forall y \exists x (x=y)$ Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP "Congratulate for" vs. "congratulate on" Which is correct?     I congratulated him for coming first in the race.      I congratulated him on coming first in the race. I keep having to re-install Ubuntu after trying advice.  This is very frustrating.  All I want is to boot to a Linux command prompt.  Please help! How can I '\input' a file without getting the implicit newline? Setup or "set up"? The word setup (as a noun), I feel, has become an acceptable part of the English language, at least insofar as technical manuals or computer textbooks are concerned. However I find that the word is used very often in verb form like so:     "You can setup the program quite easily ..."   when in fact my understanding is that the actual sentence should be:     "You can set up the program quite easily ..."   I would like to know if setup can be used as a verb. The situation seems be very similar to the word output (as a noun). Output is a purely technical word and its use is restricted solely to technical texts or at least in a technical context within non-technical books. However it is also used in verb form now like so:     "The system will output the signal ..."   I would be very grateful if this question is answered. Thank you Creating or adding geometry colunm fails even with postgis enabled Prove that $T$ is an orthogonal projection Let $T$ be a linear operator on a finite-dimensional inner product space $V$. Suppose that $T$ is a projection such that $\|T(x)\| \le \|x\|$ for $x \in V$. Prove that $T$ is an orthogonal projection.    I can't understand well. The definition of orthogonal operator is $\|T(x)\| = \|x\|$. But why that $\|T(x)\| \le \|x\|$ for $x \in V$ means orthogonal projection? I had the following two problems:     Find a counterexample for $f_*(A \cap B) \supseteq f_*(A) \cap f_*(B)$ and $ f_*(A-B) \subseteq f_*(A) -f_*(B).$ Where $f_*(X)$ is the image of $X$ under $f$ for some function $f:A \rightarrow B $ and some subset $X \subseteq A$.   I came with the following answer:  Let $ f: \mathbb{Z} \rightarrow \mathbb{Z} $, where $f: x\mapsto 0$; let $A=\{1,2\}$, and $B=\{3,4\}$.     For $f_*(A \cap B) \supseteq f_*(A) \cap f_*(B)$, $$ f_*(A \cap B) = f_*\{ \varnothing\} = \varnothing \hspace{1cm} \text{and} \hspace{1cm} f_*(A) \cap f_*(B)=\{0\} \cap \{0\} = \{0\}. $$ It follows that $ \varnothing \nsupseteq \{0\} $. For $ f_*(A-B) \subseteq f_*(A) -f_*(B)$, $$f_*(A-B)=f_*(\{1,2\})=\{0\} \hspace{1cm} \text{and} \hspace{1cm} f_*(A) - f_*(B) = \{0\} - \{0\} = \varnothing$$ It follows that $ \{0\}  \nsubseteq \varnothing $.   Now (assuming my answer is correct), let's say I want to find more counterexamples or maybe a more general answer (e.g. all the conditions under which the inclusion fails). Other than by trial and error or just intuition, how would I do that?   I know this is a broad question, so I'm specifically asking for methods or advice on how to build counterexamples in elementary set theory (for example, tips on where to begin or rules that apply in general that may be unobvious). Is there any information in canon to indicate that Dumbledore knew that the Marauders were Animagi? Is there any information in canon (or from JKR) to indicate that Dumbledore knew that three of the Marauders were Animagi?  I can't recall anything, but Harry seems to be firmly convinced that Dumbledore knows "everything that goes on around here," and that assessment seems to be accurate during Harry's years. This is a question that has been addressed several times, not only here, but also in other sites of the stack exchange network (e.g. ). However, I cannot make any of the solutions work for me.  I'm running a command through ssh. Whenever I exit ssh, I want the command to die as well. This command is a daemon called ktserver that runs indefinitely until you press Ctrl-C.  I run it as follows: ssh -t compute-0-1 ktserver and, indeed, when I press Ctrl-C, the process ends gracefully and the ssh session ends.  However, if instead of pressing Ctrl-C, I kill the ssh process using the kill command (for example, sending SIGINT or SIGHUP), the ktserver process stays alive.  How can I make the ktserver always die independent on how ssh is killed?  EDIT: If, instead of ktserver I run something completely different, such as gedit, everything works like a charm (i.e. gedit dies when the connection dies). Therefore, there might be something wrong with the process itself. For example, I thought that it might be ignoring SIGHUP or SIGINT. However, when I run kill -1 ktserver or kill -2 ktserver, the process dies as expected.  EDIT2: As Mark Plotnick points out, the issue is related to the fact that there is no communication circulating on the ssh channel. I've confirmed by running ssh -t &lt;host&gt; read and killing the ssh process afterwards. readwas still alive and kicking. Fixed background image with ios7 I am starting to learn some Regex, therefore I use this command repeatedly:  grep pattern /usr/share/dict/american-english    Only the part with pattern changes, so I have to write the long expression "/usr/share/dict/american-english" again and again.   Someone made the remark that it is possible to expand an argument of a command from the command history by typing cryptic character combinations instead of the full expression.  Could you tell me those cryptic character combinations ? So I recently saw add comment (requires 50 reputation) on a deleted answer. After looking around a bit, it seems to be on all deleted posts now (only deleted posts, normal posts still say just add comment).  I'm sure it wasn't there before (I think it just said add comment (unclickable) or possible nothing).  It is also on , presumably the root cause is the same.  And yes, I do have more than 50 reputation (in case anyone was wondering).  Just to clarify, requires 50 reputation obviously shouldn't be there for users with 50 or more reputation. Choices:   Display nothing Unclickable add comment - probably not ideal Unclickable add comment (disabled for deleted posts) or something along those lines   FYI - You may be somewhat confused right about now if you can't  yet. Electrostatics and tv screens What graphics packages are there for creating graphics in LaTeX documents?