Why the poor Wizard Families(like Weaseleys) do not turn to the muggle world to earn some easy money and then change the Muggle money back to Wizard one and get better financially. Things like    Organizing Magic shows, (The magic He/She does looks like real!!!) cheating in Casinos (well not so a good thing...) Setting up a business for any product (as you should only need a duplicating charm to create as many product as you want) and much more.    I believe there is no restriction of usage of Magic in front of Muggles for adult wizards as long as Muggles don't get too suspicious, and I don't think Muggles will start believing in a Wizarding world out of just a Magic show. Also Muggle Money can be changed into Wizarding Money at Gringotts or how else would Muggle Born have bought the Wizard things?     "Oh look Molly, they are changing Muggle Money" said Arthur looking at nervous Hermione's parents who were standing just by the counter.
Why, oh why, don't the Weasleys "conjure" up some diamonds/gold/etc, sell 'em to Muggles, and get rich? They could buy a mansion (like the Malfoys), and live there happily ever after.  I know there's  that prohibits one from conjuring food (which doesn't make much sense to me, either). Even if it applied to gold, what about all the other elements/compounds/materials? Could the law really be 'don't let a wizard conjure something if it'll make them richer'? That's totally nonsensical.  Why does Wizard society still have poor people, especially if they're talented?
Let $\{a_n\}$ be an unbounded, strictly increasing sequence of positive real numbers and let $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$. Which of the following statements is/are correct? (CSIR NET December 2014)         For all $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;1-\bf{\frac{a_m}{a_n}}$   There exist $n\geq m, \sum\limits^{n}_{k=m}x_k&gt;\frac{1}{2}$      My attempt:  Analysing question in light of $a_k=k\implies x_k=\frac{k+1-k}{k+1}=\frac1{k+1}$, I feel both are correct, I doubt if  I can generalise the result in light of this one example.   Any way to prove that this true for general case?    Note: Please do not confuse  with my question. The first two options are different, I've marked the difference in bold. Update from 14.04 to 16.04 failed with GPG error In the movies, the Death Eaters leave a smoky trail behind them as they fly. As the Order arrive in the Ministry of Magic in Order of the Phoenix, they leave a silvery trail behind them. In the books, there’s no mention of how they’re doing this. And J.K. Rowling said in the books that only Voldemort and Snape could fly like this; first seen in the Battle of the Seven Potters.  Please can somebody explain how the Death Eaters are able to fly like this? How should I parse the sentence "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo." How do Belgian fries differ from the French fries we are accustomed to eat in the US and Canada in such places as McDonald's, Wendy's, Burger King and so on? Is it the variety of potato, the preparation involved or something totally different? What oil do they use in Belgium?   I remember having them while I was visiting family in Belgium. The fries were somewhat crispy and thicker than over here. Example where union of increasing sigma algebras is not a sigma algebra I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$ I'm struggling to find the limit at infinity of : $$\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}), n\in\Bbb N$$ I know it is $1$ but I don't understand why this is wrong :  $\sin^2(\pi\sqrt{n^2 + n}) = \sin^2(\pi*n\sqrt{1 + \frac{1}{n}})$.  So $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}) = \lim \limits_{n\rightarrow\infty}\sin^2(\pi*n\sqrt{1 + \frac{1}{n}}) =  \lim \limits_{n\rightarrow\infty} \sin^2(\pi*n) = 0$.  Thanks. Using a variable in a SELECT statement? public static void handleCaseComment(CaseComment caseComment) {    User[] users = [SELECT LastName FROM User WHERE Id = caseComment.CreatedById LIMIT 1]; }   This gives me the following error:  unexpected token: 'caseComment.CreatedById'   How do I use the value of the variable caseComment.CreatedById in a SELECT statement? Fell for fake sugar daddy. How do I get out? Why doesn't grep using pipe work here? I have the following command:  find / -name libGL.so.1   Which returns lots of lines with "Permission denied". I want to exclude such lines, so I added the following:  find / -name libGL.so.1 | grep -v 'denied'   But the output is the same - my grep -v 'denied' is not filtering out the lines with Permission denied. I've tried many variations, looked over grep tutorials, but I cannot figure out the problem. Any suggestions? Why are neural networks becoming deeper, but not wider? In recent years, convolutional neural networks (or perhaps deep neural networks in general) have become deeper and deeper, with state-of-the-art networks going from 7 layers () to 1000 layers ( in the space of 4 years. The reason behind the boost in performance from a deeper network, is that a more complex, non-linear function can be learned. Given sufficient training data, this enables the networks to more easily discriminate between different classes.  However, the trend seems to not have followed with the number of parameters in each layer. For example, the number of feature maps in the convolutional layers, or the number of nodes in the fully-connected layers, has remained roughly the same and is still relatively small in magnitude, despite the large increase in the number of layers. From my intuition though, it would seem that increasing the number of parameters per layer would give each layer a richer source of data from which to learn its non-linear function; but this idea seems to have been overlooked in favour of simply adding more layers, each with a small number of parameters.  So whilst networks have become "deeper", they have not become "wider". Why is this? I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1 &amp; 20), I have written for the program to display all Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 displays = First 20 Fibonacci numbers). I thought I had a sure-fire code. I also do not see why this is happening.  startNumber = int(raw_input("Enter the start number here ")) endNumber = int(raw_input("Enter the end number here "))  def fib(n):     if n &lt; 2:         return n     return fib(n-2) + fib(n-1)  print map(fib, range(startNumber, endNumber))   Someone pointed out in my Part II (which was closed for being a duplicate - ) that I need to pass the startNumber and endNumber through a generator using a while loop. Can someone please point me in the direction on how to do this? Any help is welcome.    I'm a learning programmer and I've run into a bit of a jumble. I am asked to write a program that will compute and display Fibonacci's Sequence by a user inputted start number and end number (ie. startNumber = 20 endNumber = 100 and it will display only the numbers between that range). The trick is to use it inclusively (which I do not know how to do in Python? - I'm assuming this means to use an inclusive range?).  What I have so far is no actual coding but rather:   Write Fib sequence formula to infinite Display startNumber to endNumber only from Fib sequence.   I have no idea where to start and I am asking for ideas or insight into how to write this. I also have tried to write the Fib sequence forumla but I get lost on that as well. This thing came up in a combinatorics course I am taking.  Choose a fixed set of primes $p_1,p_2,\dots,p_k$ and let $A_n$ be number of integers in $\{1,2,\dots,n\}$ which are not divisible by any of the $p_i$'s. $A_n$ is given by $ n - \sum_{1\leq i_1 \leq k} \lfloor \frac{n}{p_{i_1}} \rfloor + \sum_{1\leq i_1 &lt; i_2 &lt; k} \lfloor \frac{n}{p_{i_1}p_{i_2}}\rfloor - \dots $. Now, if $n$ is divisible by each of the $p_i$'s then we have the simpler expression : $A_n = n \prod_{i=1}^{k}(1-\frac{1}{p_i})$(added later : note I am not assuming $n = \prod_{i=1}^{k}p_i$ here, this holds true whenever $n = c \prod_{i=1}^{k} p_i $ for some integer c, since each $\lfloor \frac{n}{p_{i_1} \dots p_{i_j}} \rfloor = \frac{n}{p_{i_1} \dots p_{i_j}}\ )$.  Another student pointed out that even if $n$ does not have $\prod_{i=1}^{k} p_i$ as a factor, the approximation $B_n = n \prod_{i=1}^{k}(1-\frac{1}{p_i})$ to $A_n$ is quite close in some specific cases. It is easy to see that $\lim_{n\to\infty}\frac{A_n - B_n}{n}=0$ as $\lim_{n\to\infty}\frac{1}{n}\lfloor \frac{n}{p_{i_1}p_{i_2}\dots p_{i_j}} \rfloor \to \frac{1}{p_{i_1}p_{i_2} \dots p_{i_j}},$ however that is not strong enough to imply that $A_n - B_n$ will be always close. Is there any way to analyze how well this approximation will perform in general? I am interested in the worst case for small to moderately sized $n$.  Just to give a feel of how close $A_n$ and $B_n$ can get, assuming the set of primes is $\{2,3,7\}$ we have (assuming my program is correct):  n     A(n)     B(n) 17    5    4.86   27    8    7.71   37    11      10.57   107   31      30.57   1111  318     317.43   3001  858     857.43   4007  1145    1144.86   5000  1429    1428.57 . Efficient evaluation of functions defined by NIntegrate Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$ I want to prove this equation, $$ \binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a} $$ I thought of proving this equation by prove that you are using different ways to count the same set of balls and get the same result. But I'm stuck. Help me please.   (Presumptive) Source: Theoretical Exercise 1.14(a), P19, A First Course in Pr, 8th Ed, by S Ross. If column matches another file, print every line with match (awk/grep) If $A$ is a non-empty set, then $A \notin A$ Exercise 3.2.2 Use the axiom of regularity and the singleton set axiom to show that if $A$ is a set then $A \notin A$.  Axiom of Regularity: If $A$ is a non-empty set, then there is at least one element x of A which is either not a set, or is disjoint from A.  Singleton Set Axiom: If $a$ is an object, then there exists a set $\{a\}$ whose only element is $a$, we refer to $\{a\}$ as the singleton set whose element is $a$ Furthermore, if $a$ and $b$ are objects, then there exists a set $\{a,b\}$ whose only elements are $a$ and $b$    I think I can give the proof when A is the non-empty set which contains finite elements. However, can anyone give any hint for the general case?  Suppose $A \in A$   Then eixsts $x$ such that either $x$ is not a set or $x \cap A$=$\emptyset$  Then it is clear thar $x \ne A$ (if $x = A$, then $x \cap A \ne \emptyset$)  We observe that as an element, $A$ $\ne$ $x$, $A$ $\in$ $A$  Then $A$ $\in$ $A-x$   Define the new set $A-x$ as $A_1$  then exists $x_1$ such that $A \in A_1-x_1$  After finite steps  we find that $A \in \emptyset $  which leads to contradiction. I keep getting the message MobileMe Service Stopped Working each time I open Outlook 2007. I have to click on the Close Program button in the error message twice each time it shows up while Outlook is trying to load up. Then I am able to use Outlook. I never use my iCloud account and would like to know how I can deactivate iCloud so I do not have issues with my Outlook. Why don't we allow low reputation users to insert more than two images in their posts? I was searching for privileges one can get after a certain amount of reputation, and I ended up with this question in my mind: Why don't we allow users with low reputation to insert more than two images or links in their posts?  Is it good to make restrictions for them? Let's say someone is going to post a good question and he/she needs to insert three images to explain it properly; because this can't be done the question may become vague or incomplete to answer, and ultimately be flagged by others. Is this a rational decision for those users?  Yes, I believe that restrictions should be there to make a control over new users like for voting privileges but is it good to make restrictions on Questions and Answers?  Here is my question:  Is it decent to restrict new users in such a manner?