Purpose of header files in cpp
Why have header files and .cpp files?
Is there an IDictionary implementation that, on missing key, returns the default value instead of throwing? Intraclass correlation coefficient vs. F-test (one-way ANOVA)? Mouse Pointer Locator Due to a stroke, I have had some vision impairment in that I sometimes have a hard time locating my mouse pointer on the screen.  I have tried making the mouse pointer larger which helps but is still not the solution.  I am new to the Mac world and would appreciate your help.  In Windows, there is an option where pressing the CTRL key will help to identify the mouse pointer using a temporary display of several radiating concentric circles around the mouse pointer.  Is there something like this on OS X? Does "corresponding author" carry an implied meaning? Study the following limit: $$ \lim\limits_{ (x,y,z) \to (0,0,0) } \frac{xy-z^2}{x^2+y^2+z^2} $$   I'm not sure if this way of proving that the limit does not exist is correct so I'm this is basically for a proof verification.  Approaching $(0,0,0)$ through the plane $z=0$, then the limit becomes  $$ \lim\limits_{ (x,y) \to (0,0) } \frac{xy}{x^2+y^2} $$  Now this limit does not exist, because approaching $(0,0)$ through the line $y=0$, the limit becomes  $$ \lim\limits_{ x \to 0 } \frac{0}{x^2} =0$$  But if we approach $(0,0)$ through the line $y=x$ we have that  $$ \lim\limits_{ (x,x) \to (0,0) } \frac{x^2}{2x^2}=\lim\limits_{ (x,x) \to (0,0) } \frac{1}{2} =\frac{1}{2}$$  So the limit $ \lim\limits_{ (x,y) \to (0,0) } \frac{xy}{x^2+y^2} $ doesn't exist. This means that the limit we began with doesn't exist, correct? How do I enable or disable the global application menu? I'm fairly excited for Unity, as it looks like a promising new direction for Ubuntu.  However, I do have a concern - will it be possible to use Unity without the global menu?  I have my window manager set to focus-follows-mouse/sloppy focus, and find the productivity gains to be immense. Sloppy focus is incompatible, however, with global menus, as it is possible for the focus to change while you move from window to menu.  Will Unity support an option to use window menus while still using Unity? Why is Minecraft giving an OpenGL error? I recently got Minecraft but not from the website, I paid for a code and everything seemed ok. When I tried to play the game a thing came up saying it crashed and then a message popped up saying The game crashed whilst initializing game     Error: java.lang.IllegalStateException: GLFW error 65542: WGL: The driver does not appear to support OpenGL. is_active_sidebar() Always Returns False What’s the rule to decide whether you add -er or whether you add -or when creating an agent noun from a verb?    Sometimes it’s -er:      read > reader hate > hater hit > hitter   But other times it’s -or:    meditate > meditator collect > collector How to learn commutative algebra? setting up apache2 webserver -- differences between behaviour within my intranet and outside Why not use the Lagrangian, instead of the Hamiltonian, in nonrelativistic QM? This is a generic inquiry on the common practice/standard for determining the acceptable values of RMS when georeferencing topographic maps.  Is there an absolute value?  Some literature suggests that it should be "less than or equal to 1/2 of the side of a cell which make up the total resolution of the image." Should I test private methods or only public ones? Problem:  Ajax suggest-search on [n] ingredients in recipes. That is: match recipes against multiple ingredients.  For instance: SELECT Recipes using "flower", "salt" would produce: "Pizza", "Bread", "Saltwater" and so forth.  Tables:  Ingredients [     IngredientsID INT [PK],     IngredientsName VARCHAR ]  Recipes [     RecipesID INT [PK],     RecipesName VARCHAR ]  IngredientsRecipes [     IngredientsRecipesID INT [PK],     IngredientsID INT,     RecipesID INT ]   Query:  SELECT     Recipes.RecipesID,     Recipes.RecipesName,     Ingredients.IngredientsID,     Ingredients.IngredientsName FROM     IngredientsRecipes      INNER JOIN Ingredients     ON IngredientsRecipes.IngredientsID = Ingredients.IngredientsID      INNER JOIN Recipes     ON IngredientsRecipes.RecipesID = Recipes.RecipesID WHERE     Ingredients.IngredientsName IN ('salt', 'water', 'flower')   I am currently constructing my query using ASP.NET C# because of the dynamic nature of the WHERE clause.  I bites that I have to construct the query in my code-layer instead of using a stored procedure/pure SQL, which in theory should be much faster.  Have you guys got any thoughts on how I would move all of the logic from my code-layer to pure SQL, or at least how I can optimize the performance of what I'm doing?  I am thinking along the lines of temporary tables:  Step one: SELECT IngredientsID FROM Ingredients and INSERT INTO temp-table  Step two: SELECT RecipesName FROM Recipes joined with IngredientsRecipes joined with temp-table.IngredientsID Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$ Suppose that $H$ and $K$ are normal subgroups of a group $G$ such that $HK=G$. I need to show that  $G/(H\cap K)\cong (G/H)\times (G/K)$.  So from the second isomorphism theorem we have that:  $HK/H\cong H/(H\cap K)$ which gives that $G/H\cong H/(H\cap K)$  $HK/K\cong K/(H\cap K)$ which gives that $G/K\cong K/(H\cap K)$  So we must now show that:  $H/(H\cap K)\times K/(H\cap K)\cong G/(H\cap K)$  So consider the map $\theta:H/(H\cap K)\times K/(H\cap K)\rightarrow G/(H\cap K)$ such that $\theta(h(H\cap K)\times k(H\cap K))=hk(H\cap K)$  Now this is a homomorphism and is surjective. To check injectiviy we see that if:  $\theta(h_1(H\cap K)\times k_1(H\cap K))=\theta(h_2(H\cap K)\times k_2(H\cap K))$ then we have that:  $(h_1k_1(H\cap K))=(h_2k_2(H\cap K))$ so that $(h_1k_1)(h_2k_2)^{-1}(H\cap K)=(H\cap K)$ which gives that $h_1k_1(H\cap K)=h_2k_2(H\cap K)$ So we are done.  Is the above correct?  Thanks for any help This is a  about Connection Refused    We see a lot of questions to the effect      When I try to connect to a system I get a message      Connection refused      Why is this ? Novel, group transported to a fantasy world, wild/chaos magic I was reading  and was strongly reminded of a series I remember reading in my teens.  This would have been a series of novels (possibly just one), published in English, and likely before 1980 - I read it in the 90s and it was fairly old, a used book.  I do not think it is the same as the linked question, which is why I'm asking this separately.  It was definitely a fantasy, not sci-fi.  Plot:  At least two girls (and possibly also some boys/other girls) are transported from modern Earth into a fantasy world.  I think they're a group of friends, possibly with some romantic pairings, and are in the 16-25 age range.  The first significant scene I remember is two of the girls ending up in a city, where they are taken in by an older female artist (might have been a different creative type, like a sculptor/actress).  She's lesbian/bisexual.  At some point she attempts to give one of the girls a love potion, but they reverse it on her, so instead the artist falls in love with the girl and accompanies her for the rest of the books.  Twist: It's later revealed that the artist's friends recognized the love potion and removed it.  She pretended to be in love and went along because she thought it would be interesting.  At some point at least one of the girls ends up basically being a magical sex slave/prostitute.  I remember her being tattooed or painted - I think in blue - and also possibly given some magical jewellery/piercings that ensure her obedience/love of her owner.  I do not remember much of the over-arching plot, just a few disjointed pieces:  The world has chaos/wild magic storms.  The books might have called them something else.  Anyone or anything caught by these storms is transformed into something else entirely, so different objects or species.  These show up throughout as minor plot encounters.  I think they can be defended against with a special material.  Near the very end, a large storm engulfs a major city, giving it entirely new architecture and transforming the inhabitants into green, hermaphrodites with a centaurish body structure.  I am not 100% sure this was the same novel, but I recall a secondary character with a secret - at night he turns into a woman (not just his body, but an entirely different person).  At some point it's revealed that the woman was his lover, and he saved her life by sharing his body with her - of course, now they can never meet/touch again. Is Switching the Neutral OK? What’s the worst that can happen if i put a switch in the neutral instead of the phase?   I just found out that 3 light bulbs sockets in my home  are connected this way, it first came to my mind to fix it but then I recalled the flow of current from positive to negative is just a convention since the electrons are charged negatively and they actually flow from N to L so i cant really find an solid excuse to mess with the wiring for the next 2 hrs How do I manage (add/remove) all the startup applications in Ubuntu 11.10 and up?  Startup Applications doesn't show all the applications which are started during boot.