Are wands required for an animagus transformation? If so, how were they used in Azkaban? If not, why did Pettigrew need one? In chapter 20 of Harry Potter and the Prisoner of Azkaban, it's made very clear that Peter Pettigrew needed a wand to use his animagus transformation and escape. However, one chapter earlier we learn that Sirius Black was using and reverting his animagus transformation inside of Azkaban. This gives us the absurd conclusion that Azkaban's prisoners have wands. Clearly, something is wrong here. What's the solution? I could speculate that it can be done without a wand but Pettigrew, unlike Black, lacks the competence, but I'm hoping for something more solid and clearly present in the text.
Animagi (Sirus specifically) and wands? I have 3 questions about animagus transformation and wands      Does animagus transformation require the use of a wand?   If yes, where does the wand go after the wizard transforms?   Again, if 1 is yes, how did Sirius transform into a dog in Azkaban?     Note that 2 and 3 are invalidated if the answer to 1 is no. If so, is it mentioned anywhere in the books, or can be implied by something in the books, that wand use is not required? I don't think Sirius managing to do it in Azkaban can be used as a proof here, as in Book 3 Wormtail needs a wand to change back into a rat
How can I unlock a password locked rar file without knowing the password? I have .rar file that is password protected, but I accidentally have forgotten the password. The file extremely important to me.  How can I get my file back? In windows, there was many programs that could remove the password of such a file. Is there one for Ubuntu? Question of remainder on dividing by 7 Question :  What is the remainder when   $$ 10^{10} + 10^{10^2} +10^{10^3} + \ldots + 10^{10^{100}} $$  is divided by $7$? Comparing complex numbers If $a+ib$, $c+id$, $e+if$ are three complex numbers, than can we tell which one is greater or smaller between them? If yes, then how and if no then why not?   Can somebody give explanation on this.... I will be grateful to him. Show that every group of prime order is cyclic Show that every group of prime order is cyclic.   I was given this problem for homework and I am not sure where to start. I know a solution using Lagrange's theorem, but we have not proven Lagrange's theorem yet, actually our teacher hasn't even mentioned it, so I am guessing there must be another solution. The only thing I could think of was showing that a group of prime order $p$ is isomorphic to $\mathbb{Z}/p\mathbb{Z}$. Would this work?    Any guidance would be appreciated. How do hashes really ensure uniqueness? This might seem an impractical and unnecessary conversation, but I feel it's something I need to clarify. Especially, as I just got my first developer job in a blockchain startup.  So hashes are said to generate the same thing for any information it sees, and it's only a one-way interaction.   As far as I understand, hashes are just long alphanumeric strings. If one computes hashes across all documents, keys, information, files, etc, over and over again- it's simply a matter of time until the same combination comes up again for different information (applying it across all possible contexts)? This might be an impractical test given size and possibility, yes, but is it this that makes hashes powerful, that it's practically impossible to recreate a hash that for any foreseeable endeavor it's fine, or is there some element that I'm missing that reduces even that extremely low probability to zero? Is there any design constraint that prevents a very powerful computer to back-calculate the original data from a hash? Or is it simply that the design is so complex that it's simply a futile exercise to dream of such a large computer required for this task? What's stopping a hacker or malicious middle man to hack open the software program or library that creates this "hash" and then use that library to create hashes of his/her own or mislabel some target company's hash with his/her own pointing to their version of the file? Especially since many applications, languages, and developers use hashing independently. Whichever is most weakly secured, we can use that to take on the rest?   Any resources are also appreciated. How can I make sure that my on-screen colors are consistent? I designed a mockup on my LG monitor. When I view the same design on another monitor that I own, the colors seem drastically different. I reset both of the monitors to their factory defaults, but still the issue persists. I'm wondering if some of my clients might dislike my designs because of this. What should I do?  How can I make sure that what I design is what my client sees?  Even worse still, I've realized that my laptop is showing different colors too. I'm a new blender user, but have used other modelling programs before.   I've downloaded a  and unzipped it.   When I import the obj into blender, it is my understanding (from here: ) that the mtl should just import itself with it. However, when I import the obj, I just get a grey model with no texture. Is it actually importing the mtl but I'm not seeing it? Also for the record, I have changed no settings in blender.  Picture for reference: Cardinality of equivalence relations on N How to catch creation of DOM elements and manipulate them with jQuery I would like to ask for some simple examples showing the uses of &lt;div&gt; and &lt;span&gt;.   I've seen them both used to mark a section of a page with an id or class, but I'm interested in knowing if there are times when one is preferred over the other. Finding the confidence level and number of successes? Given that the sample size is $1500$ and the confidence interval of $p$ is $(0.050, 0.083)$. Find the confidence level and the number of successes.  I have so far that $E=Z_{1-\alpha/2}∗\sqrt{(p∗({p-1}))/n}$   Where $p$ is the center of the given interval, so $p = (0.050+0.083)/2 = 0.0665$  Also, the error $E$ as the difference of the midpoint and the endpoint of the interval so $E=0.0665-0.050=0.0165$   Plugging this into the equation I got that  $0.0165=Z_{1-\alpha/2}*\sqrt{((0.0665)(1-0.0665))/1500}$   Solving for $Z_{1-\alpha/2}$ gives $Z_{1-\alpha/2}=2.56$ and since $Z_{2.96} = 0.99$   $Z_{1-\alpha/2} = 0.01$  Is what I have so far right? If so, how do I find the number of successes? Is it just to multiply 0.99 by the number of trials?   So that way I would get $1500*0.99=1485$ ? Why does GPS depend on relativity? Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $. Let $\{K_n \}_{n \in \mathbb{N}}$ be a collection of sets, where $K_n = [n, \infty)$. Why is $\bigcap_{n \in \mathbb{N}} K_{n}$ empty? This question is related to Exercise 2.15 in Baby Rudin, in which the reader is instructed to "[s]how that Theorem 2.36 and its Corollary become false (in $R^1$, for example) if the word 'compact' is replaced by 'closed' or by 'bounded.'"  The relevant theorem and corollary are as follows:  Theorem 2.36: If $\{K_{α}\}$ is a collection of compact subsets of a metric space $X$ such that the intersection of every finite subcollection of $\{K_{α}\}$ is nonempty, then   $\{K_{α}\}$ is nonempty.  Corollary: If $\{K_{n}\}$ is a sequence of nonempty compact sets such that $K_{n}$ contains $K_{n+1},  (n = 1, 2, 3, ...)$, then   $K_n$ is not empty.  My Question: I realize this question and similar ones have been asked elsewhere on MSE, but I've yet to see a straightforward (to me, at least) answer to my question specifically. Usually, for the "closed" part of the exercise, the following collection of closed sets, $\{K_n \}_{n \in \mathbb{N}}$ is used:  $$K_n = [n, \infty), n \in \mathbb{N}.$$  For, the intersection of every finite subcollection of ${K_n}$ is clearly nonempty. Indeed,  $$ \bigcap_{i=1}^{m} K_{n_{i}} = [N, \infty) $$  where $N = \max\{n_1, n_2, ..., n_m\}$.  Then, the assertion is made that   $$ \bigcap_{n=1}^{\infty} K_n = \emptyset. $$  However, I don't see how the same argument can't simply be used, i.e., that, for example, $N \in  \bigcap_{n=1}^{\infty} K_n$ (or maybe, say, $n+1$). Intuitively, this certainly makes sense, I'd say. For, given the archimedean property, it seems that as $n$ approaches infinity, we can always find an $l$ in each increasingly smaller set such that $n &lt; l &lt; \infty$; and so $l \in  \bigcap_{n=1}^{\infty} K_n$.  What is it exactly that I'm misunderstanding or overlooking here? How to Query all opportunities ids from account I write a sample query to fetch account Ids from cases of a particular record type.Then i wrote another sample query parent to child relationship to fetch opportunity ids from accounts.  My sample code  List&lt;Case&gt; c=new List&lt;Case&gt;(); c=[Select Id,accountId from case where RecordTypeId = '01290000000sF3L']; List&lt;Id&gt; accountIds= new List&lt;Id&gt;(); List&lt;Account&gt; accounts=new List&lt;Account&gt;(); List&lt;Opportunity&gt; opps=new List&lt;Opportunity&gt;(); for(Case cl:c)  { accountIds.add(cl.accountId); } accounts=[Select Id,name,(select Id,name from opportunities) from account        where Id in:accountIds]; System.debug('Data in accounts '+accounts);   But my issue is how to get opportunity id from above Soql accounts means how to add those opportunity id's to the list.  for(Account ao:accounts) { //How to fetch Opportunity ids from above account list. } The distance between touching objects What is the distance between, say, a cup of coffee and the table it rests on? What is the distance between two touching hands? Decision boundaries and Gaussian density functions My laptop was working perfectly yesterday, and now today I can't log in.  At first, I was only getting a black screen. However, after following instructions in some questions here on AskUbuntu, I first reinstalled lightdm, and then I had to change the ownership of the file ~/.Xauthority to be my user name. Now, I get the log in GUI screen.  However, once I enter my username, it flickers and then comes back to the login GUI. It does not matter if I use Gnome, Unity, or Gnome-Flashback.  I don't know why lightdm needed to be reconfigured, or how ~/.Xauthority got changed, but in any case, what is still standing in my way, preventing me from logging in?  Update: I have tried deleting the .Xauthority file, and the .profile files in my home directory. It has not changed anything.  Logging in as guest also fails to work.  The following commands did not work:  mv ~/.config ~/.config.BAK mv ~/.cache ~/.cache.BAK   Inside .xsession-errors in my home directory, it says:  Gdk-CRITICAL: gdk_x11_display_get_xdisplay: assertion 'GDK_IS_DISPLAY (display)' failed Debugging automatic properties Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction?