On page 140 of , author Bruno Bettelheim writes:     The verses Falada speaks three times—each time in response to the goose   girl’s lament on encountering its head: “Oh, Falada, thou who hangest   there”—do not so much bemoan the girl’s fate as express the helpless grief    of her mother.  Falada’s implied admonition is that not only for her sake,   but also for her mother’sd, the princess should stop accepting passively   whatever happens to her.  It is also a subtle accusation that, had the   princess not ated so immaturely in dropping and losing the handkerchief and   in letting herself be pushed around by her maid, Falada would not have been   killed.  All the bad things that happen are the girl’s own fault because she   fails to assert herself.  Not even the talking horse can help her out of her   predicament.   I really had difficulty in understanding what that paragraph's first sentence means, the one that without the part surrounded by dashes runs      The verses Falada speaks three times do not so much bemoan the girls fate as express the helpless grief of her mother.   Does it mean one of these three?   Falada doesn't bemoan the girl's fate as her (the girl's) mother does. As Falada expresses her (the girl's) mother's helpless grief, he doesn't bemoan the girl's fate that much/ Although Falada expresses her mother's grief, he doesn't bemoan the girl's fate that much/   I thought if express were expressing, it would make more sense. Whatever it is, I still don't understand what it means.
I am not sure of the meaning of this sentence:     The significance of culture and identity in development has to do not so much with the cultural factor in the process of development as with abandoning Eurocentric development thinking.   I'm not sure what the use of as is supposed to convey. Does it mean "development has to do not so much ... as with abandoning", i.e. not as much as abandoning? Does the abandoning have more to do with it?  And the second question: Why does it use "has to do not so much". Why not "has not so much to do"? Is "have to" a verb?
This song by The Rolling Stones, "(I Can't Get No) Satisfaction". As a non-native speaker, I always wondered what's the exact meaning of this phrase?   Is it "I'm not getting any satisfaction" (this seems to be the most widely met translation; double negation used where single negation should have been used). Or is it "I want my satisfaction, I cannot leave without getting some" (makes much more sense to me).   Or is it something else? I've always had troubles understanding double negation as applied to English. First I was taught it's a mistake to use double negation at all, and then I see it everywhere. Proving that $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c)$ where $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k<c<y_k$ Question.  Suppose that a function $f$ is defined on an interval $I$, $c$ is a point of $I$, and {$x_k$} and {$y_k$} are any two sequences in $I$ such that $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k&lt;c&lt;y_k$ for all $k$. Prove that, if $f'(c)$ exists, then $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c).$   My Attempt.  Let $\epsilon_k=\frac{1}{k}$ be given.  For $\epsilon_1=1,$ there exists $\delta_1&gt;0$ such that $x_1,y_1\in I, x_1,y_1\in N'(c;\delta_1)$ implies $\vert \frac{f(x_1)-f(y_1)}{x_1-y_1} -f'(c) \vert&lt;\epsilon_1.$  For $\epsilon_2=\frac{1}{2},$ there exists $0&lt;\delta_2&lt;$min$\{\vert x_1-c \vert,\vert y_1-c \vert,\epsilon_2\}$ such that $x_2,y_2\in I, x_2,y_2\in N'(c;\delta_2)$ implies $\vert \frac{f(x_2)-f(y_2)}{x_2-y_2} -f'(c) \vert&lt;\epsilon_2.$  Similarly, for $\epsilon_{k}=\frac{1}{k},$ there exists $0&lt;\delta_k&lt;$min$\{\vert x_{k-1}-c \vert,\vert y_{k-1}-c \vert,\epsilon_k\}$ such that $x_k,y_k\in I, x_k,y_k\in N'(c;\delta_k)$ implies $\vert \frac{f(x_k)-f(y_k)}{x_k-y_k} -f'(c) \vert&lt;\epsilon_k.$  Then by taking the limit to infinity, we obtain $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c).$   It really took me a lot of time to finish the proof and I need this to be checked by an expert:) Is the proof okay? Any response would be appreciated! Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)?   Here is an example: 5! = 120.  Is there a way I can work out the number that must be factorialed (??) to give the answer 120? Paging SQL Server 2005 Results How do I page results in SQL Server 2005?  I tried it in SQL Server 2000, but there was no reliable way to do this. I'm now wondering if SQL Server 2005 has any built in method?  What I mean by paging is, for example, if I list users by their username, I want to be able to only return the first 10 records, then the next 10 records and so on.  Any help would be much appreciated. Shoenfield introductory mathematical logic book alternatives I was originally intending on reading Mathematical Logic by Joseph R. Shoenfield (1967) though after reading  I get the impression that despite being influential for the time it was written, there now exist many new books written from our current perspective that tend to be easier on non-experts by offering more thorough explanations for each new topic being introduced.   As of now I have a basic knowledge of abstract algebra (basics on vector spaces, rings, groups etc.) from doing elementary number theory and taking a course on linear algebra, also I have completed  a year long course on real analysis which used a lot of elementary set theory and some order theory.   With all that said, I was hoping based on my current basic knowledge of math that someone could recommend me an introductory book on mathematical logic which I could use as an alternative to Shoenfield's and which addresses Peter Smith's criticisms - any help would be greatly appreciated. Find The Last 3 digits of the number $2003^{2002^{2001}}$ Find The Last 3 digits of the number $2003^{2002^{2001}}$  BY number theory or otherwise,   Also i would like to ask is there a property observed in the numbers of the form $k^n$, where for some $k, n$ is varied then the digits of $k^n$ are periodic,  for example,  $2^n$,  its last digit is periodic with period 4, its second last digit is periodic $4\cdot 5 = 20$ its third last digit is periodic with periodic with period $20\cdot 5 =100$  I have observed this property with other numbers as well, though period might vary,for different values of $k$. Get rid of the question ban on Meta; suspend actively harmful users manually Why is "high" pronounced "hiy" but is not spelled that way? How do I log every command executed by a user? I want to monitor all user's activity in my server.  Even when the user executes a shell command from some editor like vim I want to see them in the log file.  I have checked the tool acct but it is not listing the complete commands. (Please correct me if I have missed some options which does already).  Which Linux tool I should be looking at to solve this problem? What are the Minecraft Easter eggs? I was looking at  and I didn't realize that Minecraft had some Easter eggs in it. Besides the Christmas chest Easter egg, and the sheep Easter egg, what else is there? $$T(n) = \sqrt{n} T \left(\sqrt n \right) + n$$  Master method does not apply here. Recursion tree goes a long way. Iteration method would be preferable.  The answer is $Θ (n \log \log n)$.  Can anyone arrive at the solution. What I want to achieve is very simple: I have a Windows Forms (.NET 3.5) application that uses a path for reading information. This path can be modified by the user, by using the options form I provide.  Now, I want to save the path value to a file for later use. This would be one of the many settings saved to this file. This file would sit directly in the application folder.  I understand three options are available:   ConfigurationSettings file (appname.exe.config) Registry Custom XML file   I read that the .NET configuration file is not foreseen for saving values back to it. As for the registry, I would like to get as far away from it as possible.  Does this mean that I should use a custom XML file to save configuration settings?  If so, I would like to see code example of that (C#).  I have seen other discussions on this subject, but it is still not clear to me. How to add a default item to a custom taxonomy? Wordpress default taxonomy (Categories) has the item Uncategorized by default. How to add a default item to a new custom taxonomy?  functions.php:  // === CUSTOM TAXONOMIES === // function my_custom_taxonomies() {     register_taxonomy(         'block',        // internal name = machine-readable taxonomy name         'static_content',       // object type = post, page, link, or custom post-type         array(             'hierarchical' =&gt; true,             'labels' =&gt; array(                 'name' =&gt; __( 'Blocks' ),                 'singular_name' =&gt; __( 'Block' ),                 'add_new_item' =&gt; 'Add New Block',                 'edit_item' =&gt; 'Edit Block',                 'new_item' =&gt; 'New Block',                 'search_items' =&gt; 'Search Block',                 'not_found' =&gt; 'No Block found',                 'not_found_in_trash' =&gt; 'No Block found in trash',             ),             'query_var' =&gt; true,    // enable taxonomy-specific querying             'rewrite' =&gt; array( 'slug' =&gt; 'block' ),    // pretty permalinks for your taxonomy?         )     ); } add_action('init', 'my_custom_taxonomies', 0);   EDIT: I just want to have the taxonomy item there when the theme is installed. It doesn't have to automatically be added to any empty term. Me and my friend want to build a basic 101 mob farm, but we can't decide where to put it. He says it has got to be over an ocean, I say it can just be 128 blocks above ground and it will be just fine.  So the question is:    What is the absolute ideal place for a mob spawner?  If we build it 128 blocks above ground do we still need to light up caves? If we dig a 128x128 square straight to bedrock will that make a perfect environment?   Please advise! I'm heading to India next week and have a connection in Munich, Germany. I made the mistake of booking a flight with only an hour and a half layover (freaking out!) and I'm wondering if I'll have to go through customs in Munich or if I can pass right on through. Mid 2012 MBP shuts down claiming no power with charge at 30% or 40% or more I have two mid 2012 MBPs. Sometime last year they both started randomly shutting down and showing the 'please plug me in to power' image when trying to start them up. That would be fine if the batter was at 1% or less but this happens when the battery is at anywhere from 30% to as high as 48% full. The power cycle info says 500 cycles or so. Both of them do this. They are both patched current, always. I asked Apple they suggested NVRAM PRAM and SMC reset, as expected, which had no effect. Any ideas? Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, what does the locus of $M$ form? Why does the connection time out when connecting to a server? I'm examining a proof I have read that claims to show that the Cartesian product $\mathbb{N} \times \mathbb{N}$ is countable, and as part of this proof, I am looking to show that the given map is surjective (indeed bijective), but I'm afraid that I can't see why this is the case. I wonder whether you might be able to point me in the right direction?  Indeed, the proof begins like this:  "For each $n \in \mathbb{N}$, let $k_n, l_n$ be such that $n = 2^{k_n - 1} \left(2l_n - 1 \right)$; that is, $k_n - 1$ is the power of $2$ in the prime factorisation of $n$, and $2 l_n - 1$ is the (necessarily odd) number $\frac{n}{2^{k_n - 1}}$."  It then states that $n \mapsto \left(k_n , l_n \right)$ is a surjection from $\mathbb{N}$ to $\mathbb{N} \times \mathbb{N}$, and so ends the proof.  I can intuitively see why this should be a bijection, I think, but I'm not sure how to make these feelings rigorous?   I suppose I'd say that the map is surjective since given any $\left(k_n , l_n \right) \in \mathbb{N} \times \mathbb{N}$ we can simply take $n$ indeed to be equal to $2^{k_n - 1} \left(2l_n - 1 \right)$ and note that $k_n - 1 \geq 0$ and thus $2^{k_n - 1}$  is both greater or equal to one so is a natural number (making the obvious inductive argument, noting that multiplication on $\mathbb{N}$ is closed), and similarly that $2 l_n - 1 \geq 2\cdot 1 - 1 = 1$ and is also a natural number, and thus the product of these two, $n$ must also be a natural number. Is it just as simple as this?  I suppose my gut feeling in the proving that the map is injective would be to assume that $2^{k_n - 1} \left(2 l_n - 1 \right) = 2^{k_m - 1} \left(2 l_m - 1 \right)$ and then use the Fundamental Theorem of Arithmetic to conclude that $n = m$. Is this going along the right lines? The 'implicit' definition of the mapping has me a little confused about the approach.    On a related, but separate note, I am indeed aware that if $K$ and $L$ are any countable sets, then so is $K \times L$, so trivially, taking the identity mapping we see trivially that this map is bijective and therefore that $\mathbb{N}$ is certainly countable (!), and thus so is $\mathbb{N} \times \mathbb{N}$. Hence, it's not really the statement that I'm interested in, but rather the exciting excursion into number theory that the above alternative proof provides. Can we calculate the standard error of prediction just based on simple linear regression output? The standard error of prediction in simple linear regression is $\hat\sigma\sqrt{1/n+(x_j-\bar{x})^2/\Sigma{(x_i-\bar{x})^2}}$.  My question is to calculate the standard error of prediction for $pop=1029$ just based on the following regression output. I can get all except $\bar{x}$. And I also know how to calculate the approximate standard error of prediction based on the standard errors of intercept and coefficient of $pop$, ignoring their correlation.