I answered a question, was upvoted, and then edited the question. My badge progress was immediately updated. Then I thought better of my edit and rolled it back. My badge progress remained incremented.  Just confirming this is the expected behavior, as opposed to my badge progress being decremented. Would the behavior be different if someone else had rolled back my edit?
Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a &quot;(retired)&quot; next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type.
How to change the shadow color in Blender Cycles? Google map API does not plot on different continents What test can I use to compare slopes from two or more regression models? I'm learning calculus, specifically derivatives and applications of MVT, and need help with the following exercice:      Show that, for all $n &gt; 1$ $$\frac{1}{n + 1} &lt; \log(1 + \frac1n) &lt; \frac1n.$$    I tried to follow the below steps in order to prove the RHS inequality:   Proving that $f &lt; g$ on $I$ from $a$ to $b$:  Step $1$. Prove that $f' &lt; g'$ on $\operatorname{Int}(I)$.  Step $2$. Show that $f(a) \leq g(a)$ or that $f(a^+) \leq g(a^+)$  Following the above steps, let $f(x) = \log(1 + \frac1x)$ and $g(x) = \frac1x$, for all $x &gt; 1$. One has  $$f'(x) =  -\frac{1}{x^2 + x} \quad \text{and} \quad g'(x) = -\frac{1}{x^2}.$$  We note that, for every $x &gt; 1$, $f'(x) &gt; g'(x)$. Moreover, $f(1^+) = \log(2) &lt; 1 = g(1^+).$   My problem is that I got the wrong inequality sign in Step $1$.    Looking at the solution in my textbook, the author suggests using the MVT but I don't know how to apply it in this case. Create Yosemite install disk on a Windows machine I have a 2009 Mac with a new blank SSD. I have a Snow Leopard install disk but it doesn't work (it was a replacement installer disk and has never worked), so I don't have a working OS X install.  I do have a Windows 7 machine.  How should I go about installing Yosemite? All instructions I can find require OS X at some point in the process. I can't even download it from the store unless I'm on a mac. What is a good asymptotic for $f_n = f_{n-1}+\ln(f_{n-1})$? I have removed the mentioned libraries. Then my system disconnected from NIS service and many packages are being removed. The problem is I am not even able to login in my system. When i restarted it is showing "low graphics mode error". I do not know what to do Please help me. I am a beginner to Ubuntu. Consider a common proof of the uncountability of $(0,1]$, as presented  for example:  We assume that the reals can be arranged in a sequence $x_k$, represent every number in $x_k$ by its nonterminating decimal expansion, use the diagonal argument to create a sequence of decimal digits that differs from the nonterminating decimal expansion of each number in $x_k$ and then claim that this sequence of digits so generated must be the decimal expansion of some number not in $x_k$.  My problem is with this last step. Could it not be the case that the new sequence of digits is just the terminating decimal expansion of some number already in $x_k$?  Would it not be more correct to use the sequence $x_k$ to generate a sequence of all (both terminating and non-terminating) decimal expansion of all numbers in $[0,1)$ and then apply the diagonal argument? How do I check if a string is a number (float)? What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse. Wrong user when logging into Data Explorer I think I'm having the same issue as reported in this question:    When I log into SEDE with the same OpenID account I use for SE, a different user comes up ("James Wiseman" on Stack Exchange and "adsense" in Data Explorer).  Is there anything I can do personally to rectify this, or must I rely on the admins? I am from Nigeria and I'm doing a one year Internship program with The Marriott hotel in Wisconsin, I applied for the UK visitor visa two weeks ago to visit my fiance who lives and work in the UK, but I was refused the visa because the letter of my workplace that I provided was back dated of 2014 which they say they are not satisfy it accurately reflects my current employment circumstance. I also provided my pay slips, but they said they were not satisfied with it demonstrating the terms and conditions of my employment, and they also said I did not present any evidence to satisfy me having sufficiently strong ties and commitments in my country of habitual residence or elsewhere to motivate my timely departure from the UK. They said the documents my fiance presented were OK.  How soon can I re-apply for a UK visa after getting a refusal? Name of short sci-fi story involving a musician who is punished for listening to Bach I read a short story a long time ago and I can neither remember the title nor the author.  The main character is a musician.  He is sequestered and allowed to play all day on some kind of a fantastic instrument; however, he has been barred from listening to any music for fear that it will stifle with his innate creativity.  Someone secretes him some Bach, he listens to it, and is then caught and cast out.  He gets a series of jobs and is inevitably punished for breaking some music-related taboo.  Any ideas? Change system date programmatically How can I change the local system's date &amp; time programmatically with C#? How do I remap certain keys or devices? I'm searching for a way to remap certain keys in ubuntu.  i.e.   I'd like to change PgUp to Home or PgDown to End.  Does a built-in command or a tool exist reassign keys in Ubuntu/GNOME? Can't find Corruption Problem storing arrays with update_user_meta I am writing a function that adds an ID number to an array and puts the array in the usermeta. $_GET['auction'] is the post_id.  Below is the function:  $reminders = get_user_meta( $current_user-&gt;ID, "reminders" ); print_r( $reminders ); if( in_array( $_GET['auction'], $reminders ) ) {     echo "Failed: Auction already in list"; } else {     array_push( $reminders, intval( $_GET['auction'] ) );     if ( update_user_meta( $current_user-&gt;ID, "reminders", $reminders ) ) {         echo "Success";     } else {         echo "Failed: Could not update user meta";     } } print_r( $reminders );   Here is the output after adding one auction:  Array ( )  Success Array ( [0] =&gt; 7 )    Here is the output after adding two auctions:  Array ( [0] =&gt; Array ( [0] =&gt; 7 ) )  Success Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 )   And here is the output after adding three auctions:  Array ( [0] =&gt; Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 ) )  Success Array ( [0] =&gt; Array ( [0] =&gt; Array ( [0] =&gt; 7 ) [1] =&gt; 73 ) [1] =&gt; 0 )   Notice that adding a new element to the array using array_push works fine. But when the array is stored in the usermeta then retrieved again, the last element in the array has been put into an array of its own, creating an infinitely dimensional array. I'd prefer to keep this array one dimensional.  Is there a way I can run update_user_meta and get_user_meta without it changing the structure of my array? Piping data through arbitrary functions in Clojure I have two arbitrary lines in 3D space, and I want to find the distance between them, as well as the two points on these lines that are closest to each other.  Naturally, this only concerns the skew case, since the parallel and intersecting cases are trivial.  I know how to find the distance, as the question was asked before and answered .  I haven't found a good explanation on how to find the two points that determine that distance, though.  So specifically, given two lines  $$L_1=P_1+t_1V_1$$ $$L_2=P_2+t_2V_2$$  I would like to find two points $X_1$ on $L_1$ and $X_2$ on $L_2$ such that the distance between $X_1$ and $X_2$ is minimal. integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration? I have an interest in contour integration. I am not that good at it, but I enjoy learning what I can about it.  Here is a version of a rational log integral rarely encountered.  $\displaystyle \int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx=\frac{3}{4}\ln^{2}(2)-\frac{{\pi}^{2}}{48}$  I can do this using real methods (via double integral and substitution). I can post my workings if anyone would be interested.  My question is, can this be evaluated using contour integration due to the limits being $[0,1]$ instead of $[0,\infty)$?.  Contours may not be the most efficient way to go about it, but what is the course of action when the limits are 0 to 1 instead of 0 to infinity?. I am looking for a closed form (ideally expressed as elementary functions) of the function $\exp_n(x) = \sum_{k=0}^n x^k / k!$.  I am already aware of expressing it in terms of the gamma function. Background / Motivation When counting combinations of objects with generating functions, it is useful to be able to express the partial sum $1 + x + \cdots + x^n$ as $\frac{1-x^{n+1}}{1-x}$. For example, to count the number of ways to pick 5 marbles from a bag of blue, red, and green marbles where we pick at most 3 blue marbles and at most 2 red marbles, we can consider the generating function $f(x) = (1+x+x^2+x^3)(1+x+x^2)(1+x+x^2+\cdots)$. By using the partial sum identity, we can express it as $f(x) = \left(\frac{1-x^4}{1-x}\right)\left(\frac{1-x^3}{1-x}\right)\left(\frac{1}{1-x}\right)$.  Simplify, express as simpler product of series, and find the coefficient of the $x^5$ term. I want to be able to do the same for a generating function in the form $g(x) = \exp_{n_1}(x)^{p_1} \exp_{n_2}(x)^{p_2} \cdots \exp_{n_j}(x)^{p_j}$ The easiest way to extract the coefficient of a given term $x^p / p!$ would be to use a similar closed form expression for $\exp_n(x)$ and a similar technique to $f$. Attempted Solutions Differential equation Recall that the way to prove the identity $1+x+x^2+\cdots+x^n = \frac{1-x^{n+1}}{1-x}$ is to define $S = 1 + x + x^2 + \cdots + x^n$ and notice that: $S - Sx = 1 - x^{n+1}$. Likewise, notice that $y(x) = \exp_n(x)$ satisfies $y - y' = x^n/n!$.  Via SAGE, the solution is $y(x) = \frac{c+\Gamma(n+1,x)}{n!}e^x$.  Our initial condition $y(0) = 0$ so $c=0$.  By , $\Gamma(n+1,x) = n! e^{-x} \exp_n(x)$ so we have $y(x) = \exp_n(x)$. Recurrence Relation Notice that $\exp_n(x) = \exp_{n-1}(x) + x^n/n!$. Using the unilateral Z-Transform and related properties, we find that $\mathcal{Z}[\exp_n(x)] = (z e^{x/z})/(z-1)$. Therefore, $\exp_n(x) = \mathcal{Z}^{-1}\left[(z e^{x/z})/(z-1)\right] = \frac{1}{2 \pi i} \oint_C z^n e^{x/z}/(z-1)\;dz$. $(z^n e^{x/z})/(z-1)$ has two singularities: $z = 1$ and $z = 0$.  The point $z = 1$ is a pole of order one with residue $e^x$.  To find the residue at $z = 0$ consider the product $z^n e^{x/z} (-1/(1-z)) = -z^n \left( \sum_{m=0}^\infty x^m z^{-m} / m! \right) \left( \sum_{j=0}^\infty x^j \right)$.  The coefficient of the $z^{-1}$ term is given when $n - m + j = -1$. The residue of the point $z=0$ is then $-\sum_{m,j} x^m / m! = -\sum_{m=n+1}^\infty x^m / m!$. Let $C$ by the positively oriented unit circle centered at the origin.  By Cauchy's Residue Theorem, $\frac{1}{2 \pi i} \oint_C z^n e^{x/z}/(z-1)\;dz = \frac{1}{2 \pi i} 2 \pi i \left(e^x - \sum_{m=n+1}^\infty x^m / m!\right) = \exp_n(x)$. Finite Calculus I've tried to evaluate the sum using finite calculus, but can't seem to make much progress.