Two varieties of apple      Two varieties of apples      Two varieties of an apple   Is there any difference between these. Which one should be preferred by a native speaker?
can anybody tell me which one of these is the correct one? I have been searching all over the internet but I have still got no answer.  Types of books Types of book
What does each SPECIAL stat in Fallout Shelter do? Besides its workplace uses, like Charisma in Living Quarters, Strength in Power Generators, Agility in Diners.   Do we know if Endurance increases HP in the Dwellers, or that strength helps in melee damage / survivability in the wastelands? And Perception? What should my Objective-C singleton look like? My singleton accessor method is usually some variant of:  static MyClass *gInstance = NULL;  + (MyClass *)instance {     @synchronized(self)     {         if (gInstance == NULL)             gInstance = [[self alloc] init];     }      return(gInstance); }   What could I be doing to improve this? Obi-Wan left Anakin for dead, and one movie later (in A New Hope) he was saying Anakin had been killed by Darth Vader.  What exactly did Obi-Wan know about Anakin and Darth Vader before A New Hope started? If $xy + yz + zx = 1$, then show that      $$\dfrac{x}{1-x^2} + \dfrac{y}{1-y^2} + \dfrac{z}{1-z^2} = \dfrac{4xyz}{(1-x^2)(1-y^2)(1-z^2)}$$   I tried doing the sum algebraically, that is, by solving the LHS but, that method isn't really getting us anywhere.  Also, I found this sum in an a book on trigonometry. So how can I solve it with trigonometry? What is the opposite of "personification"? I want a word that means the opposite of personification.  What is the correct word for describing people with the characteristics of an object/as if they are objects?  I found the word chremamorphism on some forums, but it doesn't seem to be included in the two online dictionaries I searched. How do I change the email address used for Google Play? My email address I use for the Play Store will be invalid soon, so I need to change it. However I don't want to make a new account because I want to keep all my apps. How can I do that? How to explain in layman’s terms the significance of the difference of qubits of the D-Wave and IBM QX? So, @AndrewO mentioned recently that he has had 'encounters' with people wondering why D-Wave has a lot more qubits than IBM. Of course, this comparison is faulty, since the IBM and D-Wave's machine may both exploit quantum effects to a certain degree, IBM's machine matches the thing the TCS people call a 'Quantum computer' a bit more than D-Waves's alleged quantum annealer.   How do you explain to a novice why IBM is still reaching important milesstones, even though the D-Wave has a lot more 'qubits'. I understand that an easy answer is, 'well, you're comparing apples and pears', but that is merely relying on your possible authority and simply doesn't explain anything!   How can you explain that those devices are different, how can you dispell the myth that the number of qubits is not the only metric to judge quantum devices? (preferably to a layman, but assuming basic (undergrad?) physics knowledge is ok, if needed) Let $a,b,c$ be $3$ distinct integers, and let $P$ be a polynomial with integer coefficients.Show that in this case the conditions $$P(a)=b,P(b)=c,P(c)=a$$ cannot be satisfied simultaneously.  Any hint would be appreciated. Django: How can I protect against concurrent modification of database entries Let $\{a_n\}$ be defined as follows: $$a_1 = 2, a_{n+1}=\dfrac{1}{3-a_n}$$ $n \geq 1$.   Does $\{a_n\}$  converge?    Using the monotone convergence thereom, if the sequence is both bounded below and decreasing, $\forall n\in\mathbb{N}, n\geq 1$, then we can say the sequence converges.  I'm having trouble proving that the sequence is bounded below by induction.    Claim: The sequence is bounded below by $0$.  Base Case:  $n=1$  $a_1 = 2 \geq 0$, so this holds.  Induction Step  Suppose that $a_k \geq 0$, for some $k \in\mathbb{N}$. (IH)  Prove $a_k \geq 0\to a_{k+1} \geq 0$  I have some difficulty here.  $a_{k}=\dfrac{1}{3-a_{k-1}} \geq 0$  $a_{k+1}=\dfrac{1}{3-a_{k}}$, but we know $a_k \geq 0$, but we don't know how much bigger. It could be that $a_k = 4$, and then I have $a_{k+1}=\dfrac{1}{3-4}$, which is negative, and does not confirm with my claim of being bounded below by $0$. Have I gone somewhere wrong in my induction? Show that $a(-1) = (-1)a = -a $. In a ring $R$ with identity 1, show that $$a(-1) = (-1)a = -a \qquad\forall\, a \in R$$ I have started with $a + (-a) = 0$ but cant proceed from here. Okay, this should be super easy to do but I just can't find the way.  I have a background image with a solid colour layer on top of it, and I would like to add text on top of everything in such a way that the filling of the text is the image in the background. I have tried selecting the text shape and deleting that selection shape in the solid colour layer, but it just looks wrong.   Can anyone help me with this? Many thanks in advance. number of prime ideals in algebraic integers Down vote changed to up vote caused reputation meter to pass daily maximum I just experienced a minor visual bug.  I had an answer that earned 2 down votes and 22+ upvotes, earning me the daily maximum of +200. Upon making some edits to the answer at the behest of the comments, one of the users who down voted changed their vote. Now my reputation meter shows that I gained +202 for the day.    This correctly did NOT affect my reputation, as I still only gained 200, so it is merely a minor display bug.  This appears in the achievements drop down and my reputation tab on my profile. I can successfully tether my Mac (10.7.3) to my iPhone4 (5.0.1) via wifi, no problem, been doing it for months.  However, when I try to tether via bluetooth instead, I can't seem to see the internet from my mac.  Network Settings reports a green light for Bluetooth PAN, but my browser can't connect to anything at all.  My Mac reports very similar IP addresses for both, starting with 172.20.10 and differing only in the last octet.  Any idea why I can't successfully tether via bluetooth? How did Suren Manvelyan create the macro pictures of eyes? I came across some really cool  today. How did he manage to get these photos? I couldn't find any EXIF information anywhere, and I don't have enough experience with macro to figure out how he did it.  It's obvious that the light has a lot to do with the result. How and what kind have been used? And what kind of camera equipment? Recursively copy files from one directory to another I have all my music in a folder /media/kalenpw/MyBook/Music/ABunchOfOtherFoldersWithFilesInside. I want to copy all of the mp3s to /media/kalenpw/HDD/Music so I used:  cp -R /media/kalenpw/MyBook/Music/*.mp3 /media/kalenpw/HDD/Music   however this only copied the mp3s in the root music folder and did not open any of the artist subdirectories and copy those files.  I was under the impression -R would recursively copy all the files. How can I achieve said goal? How to install Canon LBP2900b drivers? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.  What are good introductory guides to QM along these lines? How to use Terminal to delete all .svn folders recursively? What command can I type into the Terminal so that I can delete all .svn folders within a folder (and from all subdirectories) but not delete anything else?