Word for liking and not liking something at the same time?
Word for feeling conflicting emotions simultaneously
Old fantasy book with a party finding coloured stones having powers over fire, water, mood I'm trying to remember the name of a book series of which I remember only the following, with Google yielding no results.   the name of the author starts with a Z   the main character is a knight in an household with a name sounding like Malachai who goes on a quest with six others guys and girls (a bard, another knight, a priest, etc.) and each of them finds a stone of colour which has a power on various things (like fire, their mood or water) and then they set toward a quest to beat some ancient evil. I used to find the book at the local library 10 years ago in France (but it was translated). KDB: apply dyadic function across two lists How does a one-sided glass work? How does a  work? If seen from the outer side, we can see through thinking it is transparent, while if seen from the inside, the glass acts as a mirror. How? Induced sequence of global sections I'm reading Differential Analysis on Complex Manifolds by Raymond O. Wells. It states the following in the beginning of section 3 of chapter 2 on page 51:  Consider a short exact sequence of sheaves:  $$0 \to \mathcal{A} \to \mathcal{B} \to \mathcal{C} \to 0$$  Then it is easy to verify that the induced sequence  $$0 \to \mathcal{A}(X) \to \mathcal{B}(X) \to \mathcal{C}(X) \to 0$$  is exact at $\mathcal{A}(X)$ and $\mathcal{B}(X)$ but not necessarily at $\mathcal{C}(X)$. After that they give an example of failing exactness at $\mathcal{C}(X)$.  My problem is that Ii dont see why the induced sequence has to be exact at $\mathcal{A}(X)$ and $\mathcal{B}(X)$. I tried to find an answer in other books. In the book Sheaf Theory by Bredon they make the same statement in proposition 2.2 but they also state it is easy to verify.  I tried to come up with an argument of my own and got something like this (the argument is wrong i think): If we have the zero element  $0 \in \mathcal{B}(X)$ this should induce a section $\tilde{0} $ of the stalks of $\mathcal{B}$ and should take the value of the zero element in every stalk. Then since the sequence of sheaves is exact (and thus exact in stalk level) we get that around every $x \in X$ there should be an open $V$ such that $\tilde{0}|_{V}$ is the image of the zero section in $\mathcal{A}(V)$ and since $\mathcal{A}$ is a sheaf we can patch these together to get a global zero section.  Also while i get the example that shows inexactness at $\mathcal{C}(X)$ i dont get why this should generally be the case.  Any help would be much appreciated Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$ Find the maximum value of $f(x)$ when $0 \leq x \leq 1$ and $$ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$$   I'm guessing that the Fundamental Theorem of Calculus can't be used because the integrand is a function of $x$.  Any help would be greatly appreciated. Benefits of using backtick (`) in MySQL queries? In MySQL we can create queries with or without the backtick (`) symbol. Example:   SELECT * FROM TEST; SELECT * FROM `TEST`;   Both works fine in mysql-console.  Is there any technical difference between them?  Is there any benefit using (`) over over simple queries? What is the correct position of the word 'also'?     I would like to also talk about ...      I would also like to talk about ... I am trying to create a 3d game in unity. I have a cube in unity and I want it to move left or right on swipe . It should move to a distance till where user swipe or take their finger off of a screen. I want it to move fast or the cube should move fast on swipe and cube should flow smooth. Like in the gif there is a circle and the user use their finger to move the circle till wherever the user swipe it and it should be instant and I want my cube to move like that at a distance till where user swipe their finger and it should be instant and fast.  I don't know how to do it. Any help is appreciated! Do the parent directory's permissions matter when accessing a subdirectory? If I have a root folder with some restrictive permission, let's say 600, and if the child folders/files have 777 permission will everybody be able to read/write/execute the child file even though the root folder has 600? Is there any way to script Windows 10's "color filter" feature programmatically? How many square meters "twenty feet square" is? One would assume it to be about 2 square meters, but this is obviously not the case. In fact, I'm reading Illium by Dan Simmons. A quote follows:     Much like the room they had faxed into, this space was windowless and about twenty feet square. But unlike the other room, this one was warm, lighted, and free of snow or ice. And unlike the other room, this one was almost filled with an oval metal machine about fifteen feet long.   By this description, "twenty feet square" seems to mean 20x20 feet aka 400 square feet or 40 square meters. Given that Dan Simmons is a renowned American writer, it's not likely that he just can't speak English correctly. So, who's right and who's wrong here? "Distribution worker" vs. "distributed worker" I cannot differentiate the meanings of the two words. Could you please clarify?   In general, when should I use a noun (distribution) or an adjective (distributed) for verbs similar to distribute, like organize, create? Not to Mention ≈ [Let Alone ≈ Much Less ≈ Still Less] For brevity, I symbolise synonymity with ≈.  So  X ≈ Y  means  X and Y are synonyms.  From : let alone ≈ not to mention  From :  let alone ≈ much less ≈ still less.  Are these all synonyms? What are the similarities and differences between each? What is the difference between old style and new style classes in Python?  When should I use one or the other? I'm going down my huge backlog of unplayed Steam games and I'm thinking the best way to tackle the list is to go through the shortest games first and then concentrate on the 20+ hour ones. I'm wondering if there's a website or something else that has an estimated amount of gameplay time for games.   Is there anything like that? Why does Google not consider dot in usernames of Gmail addresses? Undefined reference to static class member Can anyone explain why following code won't compile? At least on g++ 4.2.4.  And more interesting, why it will compile when I cast MEMBER to int?  #include &lt;vector&gt;  class Foo {   public:       static const int MEMBER = 1;   };  int main(){       vector&lt;int&gt; v;       v.push_back( Foo::MEMBER );       // undefined reference to `Foo::MEMBER'     v.push_back( (int) Foo::MEMBER ); // OK       return 0; } Here is my proof, I would appreciate it if someone could critique it for me:  To prove this statement true, we must proof that the two conditional statements ("If $\mathcal{P}(A)⊆ \mathcal{P}(B)$, then $A⊆B$," and, If $A⊆B$, then $\mathcal{P}(A)⊆ \mathcal{P}(B)$) are true.    Contrapositive of the first statement: If $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$  If $A \nsubseteq B$, then there must be some element in $A$, call it $x$, that is not in $B$: $x \in A$, and $x \notin B$. Since $x \in A$, then $\{x\} \in \mathcal{P}(A)$; moreover, since $x \notin B$, then $\{x\} \notin \mathcal{P}(B)$, which proves that, if $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$. By proving the contrapositive true, the original proposition must be true.    To prove the second statement true, I would implement nearly the same argument, so that isn't necessary to write. So, does this proof seem correct? Also, was the contrapositive necessary? Or is there another way to prove the initial statement? nginx open reverse proxy? Why does C# disallow readonly local variables? Having a friendly debate with a co-worker about this.  We have some thoughts about this, but wondering what the SO crowd thinks about this?