But you're Muggle-born, so someone from the school will have to come and explain to your parents.   Okay so Harry isn't Muggle-born, but he is Muggle-raised as the Hogwarts admission committee probably knows.  Just before Harry's first year, why did Hogwarts send so many letters instead of just having Hagrid or someone go in the first place?
In Harry Potter and the philosophers stone Harry was "receiving" his letters in a way that was so labour intensive. First, one was sent in the mail, and the others where then sent, either shoved into the letterbox or through the door cracks. It then it got, "out of hand," as twenty four letters found their way inside the house. The letter sender (Minerva, I do believe, Deputy Headmistress) must, obviously have known they were not getting to Harry, so why keep sending them? I cannot even believe Minerva sending more than thirty letters! Why not either,  A) Send the letters directly to Harry  OR  B) Show up at the house, to explain everything.  Why not do a more logical way of sending/explaining Harry's being?
Number of preimages of a group element under a homomorphism. Move every file that is not a directory Evaluate $\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ Evaluate $$\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$$  We can write as $\displaystyle\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ $$= \lim_{n \to \infty}\left[\frac{(n +1)(n+2) \cdots (n+n)}{n^n}\right]^{\frac{1}{n}} = \lim_{n \to \infty}\left[(1+\frac{1}{n})(1+\frac{2}{n})\cdots (1+\frac{n}{n})\right]^{\frac{1}{n}}$$  I have used this result if $\{a_n\}$ is a sequence of positive term which is convergent to $l$ and $b_n = (a_1. a_2 . \cdots a_n)^{1/n}$ ,thhen $b_n$ converges to $l$  here $a_n = 2$, but i think it is not right,how to use this result in this question. Give me hint how to proceed . Thank you How do you fix a bad merge, and replay your good commits onto a fixed merge? I accidentally committed an unwanted file (filename.orig while resolving a merge) to my repository several commits ago, without me noticing it until now. I want to completely delete the file from the repository history.   Is it possible to rewrite the change history such that filename.orig was never added to the repository in the first place? Suppose k is an integer such that $6k + 1$, $12k + 1$, $18k + 1$ are primes. Show that $n = (6k + 1)(12k + 1)(18k + 1)$ is a Carmichael number. Suppose k is an integer such that $6k + 1$, $12k + 1$, $18k + 1$ are primes. Show that $n = (6k + 1)(12k + 1)(18k + 1)$ is a Carmichael number.  This is a question on a past exam that I find difficulty to answer. Can anyone help? does anyone know the following result? If it holds in this form and any source which presents it? Thanks a lot.  Consider metric space $(X,d_{X})$.  Let $f:A \subset (X,d_{X}) \rightarrow \mathbb{R}$ be a Lipschitz continuous function i.e. $\exists K &gt; 0$ such that  \begin{align*} |f(x)-f(y)| \leq Kd_{X}(x,y) ~~~~\forall x,y \in A \end{align*}  then define functions  $$\bar{f_{1}}(x) := \sup\lbrace f(y) - Kd_{X}(x,y): y\in A \rbrace ~~ \forall x  \in X$$ and $$\bar{f_{2}}(x) := \inf\lbrace f(y) + Kd_{X}(x,y): y\in A \rbrace ~~ \forall x  \in X$$ it follows that  \begin{align*} \bar{f_{1}}, \bar{f_{2}}: X \rightarrow \mathbb{R}  \end{align*} are Lipschitz continuous with  \begin{align*} |\bar{f_{i}}(x)-\bar{f_{i}}(z)| \leq Kd_{X}(x,z) ~~~\forall x,z \in X \text{ and } \forall  i = 1,2 \end{align*} and  \begin{align*} \bar{f_{i}}(x) = f(x) ~~~ \forall x \in A \text{ and } \forall i =1,2 \end{align*} Cycles settings missing This particular blend file is messed up. I'm not sure what I did or pressed. If I open a new blend file everything works fine but in this one the materials tab is missing and the render properties is also missing some things. I don't want to start over my project. I have tried a day and a half to figure this out. Matrix given by $a_{ij} = 1/(i+j)$ is non-singular. Filter to change the content of 404 page I have created custom rewrite rules. These rules now go to 404 page as expected. I can use action hook template_redirect to change the template matching query_var.  But I don't want to create separate template files as the page structure depend on the current theme in use. Rather I just want to change the content and title. I have tried change the content using the_content filter, but it seems the filter doesn't even get called for 404 page.  I also tried loading index.php template and then using the_content filter, but it also doesn't work.  Is there any way to achieve this? What is the difference between: Rooting, Jailbreak, ROM, Mod, etc.? find the minimum value given constraints File list command line (hidden and subfolders) Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. Error in if/while (condition) {: missing Value where TRUE/FALSE needed What should I do when Ubuntu freezes? All operating systems freeze sometimes, and Ubuntu is no exception. What should I do to regain control when...   just one program stops responding? nothing at all responds to mouse clicks or key presses? the mouse stops moving entirely? I have an    In what order should I try various solutions before deciding to pull the power plug?  What should I do when starting up Ubuntu fails?  Is there a diagnostic procedure I can follow? Can wizards really cast spells in armor? What is the SKU of a motor? I came across an 'N20' motor, and I don't know what that means. As far as I can tell (and please correct me if I'm wrong), N20 is the SKU of the motor. What is the SKU? Note that this is not the same as:   Mistagged questions should be retaggable immediately. Prove Lipschitz function $f$ with constant $K$ is integrable on $[0, 1].$ We suppose that $f : [0, 1] \rightarrow \mathbb{R}$ is a Lipschitz function with constant $K$. We want to show that $f$ is integrable on $[0, 1].$  I've been trying to use the Darboux criterion of integrability by trying to show that, for $\epsilon &gt; 0$, $$S^*(f,P) - S_*(f, P) &lt; \epsilon,$$ where $S^*(f, P)$ and $S_*(f, P)$ are the Upper and Lower Riemann Sums, respectively.  This is what I have so far: $$\sum_{i=1}^n M_i (x_i - x_{i-1})- \sum_{i=1}^n m_i (x_i - x_{i-1}) = \sum_{i=1}^n (M_i - m_i) (x_i - x_{i-1})$$ $$\le \sum_{i=1}^n K (x_i - x_{i-1}).$$ because $|f(x) - f(u)| \le K|x-u| \le K |1|$, since $x\in [0, 1]$. Then, $$\sum_{i=1}^n K (x_i - x_{i-1}) = K.$$ However, this is only a single upper bound, not an arbitrary $\epsilon.$ Can I get some pointers about how to proceed? Thanks! When documenting a style file, it would be nice to be able to easily put side by side different examples of code, side-by-side with the output they produce.  What recommendations to people have to do this efficiently, and &aelig;sthetically?