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What's wrong with this division? I think there's a lot for me to learn about data types. Why this happens  double result = ((3/8)*100).ToString();   it gives zero .. should be 37,5 ... :( Is there a tool in Ubuntu to automatically merge two images having a common strip? I need to scan a large image, which will not fit at once in the scanner. I was thinking about scanning it in two parts and hand-editing the result in Gimp to join them. But probably an automatic tool can do the same more quickly and better.  EDIT I think I may have not made my point clear. My difficulty is not aligning two images. My problem is that one has to compensate for the rotation or distortion introduced by the manual process of putting the sheet into the scanner, and an automatic tool should obtain more precise results at analyzing common patterns in the two images to rotate and align them seamlessly. Counting binary operations on a set with $n$ elements I am trying to solve following problem but not able to find any way to proceed.  Let $S$ be a set having $n$ elements. Can we count about number of binary operations that can be defined on a set? Can we also count number of commutative binary operations defined on  $S$?  Thanks for the help and suggestions I was answering a question on Stack Overflow and required to use a trailing space in one of my code snippets.  I formatted it like so:  `&lt;a `   And it renders without the trailing space: &lt;a  Using the &lt;code&gt; tag does account for trailing spaces, though in my case it busts because of the &lt;. Here's my formatting with the &lt;code&gt; tag:  &lt;code&gt;&lt;a &lt;/code&gt;   Here's how it renders:  (Yes, you should see nothing there).  This is a pretty annoying bug. Can we get it fixed? How to do relative imports in Python? Recovering from forgotten lock pattern My son has an impression tablet 10 and has forgot the lock pattern. How can we reset it without knowing the code? How do I quickly switch between weapons and spells? When  I see him quickly change his weapons and spells during combat. When he later goes inside his items, you can see a second smaller arrow next to the weapon that you can quickly change to in combat. How can I set such an alternative so that I can quickly switch weapon?  The screen doesn't seem to intuitively explain what key I need to use to do that... Suppose, I want to refer multiple equations (1), (2), (3), (4), (5) and (7) so that they appear as (1-5, 7):  \documentclass[fleqn,preprint,10pt]{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} \begin{align} \label{1}\psi([e_1,e_2]) = \psi(e_2) = e_2 = (e_2,2e_3) = (-2e_3,e_2) = (\psi(e_1), \psi(e_2))\\ \label{2}\psi([e_1,e_3]) = \psi(2e_3) = 2e_1 = (e_1,2e_3) = (-2e_3,e_1) = (\psi(e_1),\psi(e_3))\\ \label{3}\psi([e_2,e_3]) = 0 = (e_2,e_1) = (\psi(e_2),\psi(e_3)),\\ \label{4}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{5}\left\{e_1, e_2\right\},\,\,\,\left\{e_3, e_1\right\},\,\,\,\left\{e_3, e_2\right\},\\ \label{6}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{7}\text{Nor}_{L_4\oplus L_3}\left(\{e_2\}\right)/\{e_2\}=\,\{e_1, e_3, e_4\} \end{align} \end{document} I'm looking for a book that starts with the premise that (once the population size had exceeded a certain number) the future development of mankind (revolutions and wars in so and so many years, colonization of other planets in so and so many years, and so on) could be predicted completely by applied statistics. (IIRC, they used slide rules for those exact predictions, but that is certainly owed to the time the story was written). Next, the predictability was used to take a few tiny measures that would change mankind's fate in a favourable way. After a long time, the predictive system fails(?) because a mutation occurs in some person(s).  And now is the part where I'm not sure if it belongs to this or another story: The mutation results in the ability to "beam" by thinking of a place where one has been before... Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function In Walter Rudin's Principles of mathematical analysis Exercise 5.21, it is proved that for any closed subset $E\subseteq \mathbb{R}$, there exists a smooth function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$.   Since $E^c$ is open in $\mathbb{R}$, $E^c$ is a countable disjoint union of open intervals $(a_i,b_i)$. On an interval $(a,b)$, if we let $f(x)=\exp(\frac{1}{(x-a)(x-b)})$, $x\in(a,b)$; $f(x)=0$, $x\notin(a,b)$, ($f(x)=\exp(\frac{1}{(x-a)})$ or $f(x)=\exp(\frac{1}{(x-b)})$ on $(a,\infty)$ and $(-\infty,b)$ resp.), then $f$ is smooth. Hence we can get a smooth function on $\mathbb{R}$ such that $E$ is the zero point sets of $f$.  (1). How about a closed subset $E$ of $\mathbb{R}^n$? is it true that for any closed subset $E\subseteq \mathbb{R}^n$, there exists a smooth function $f$ on $\mathbb{R}^n$ such that $E=\{x\in \mathbb{R}^n\mid f(x)=0\}$?  An open set in $\mathbb{R}^n$ cannot be written as a disjoint union of countable open balls hence the proof above is not valid. The partition of unity only claims that for an  open set $U$, there exists open $V$ in $U$ such that $\bar V\subseteq U$ and a smooth function $f$ on $\mathbb{R}^n$ such that $supp f\subseteq U$, $f|_V=1$.   (2). The taylor series of $f(x)=\exp(\frac{1}{(x-a)(x-b)})$ does not converge around points $a,b$ hence $f$ is not analytic at $a,b$. Is it true that for any closed subset $E\subseteq \mathbb{R}$, there exists an analytic function $f$ on $\mathbb{R}$ such that $E=\{x\in \mathbb{R}\mid f(x)=0\}$? I'm looking for a word that means     someone (especially a boss) who is not pleased (with your work, attitude etc.) no matter how hard you try. To better describe the above problem, whenever I start up my Ubuntu/Windows 10 Machine and select Ubuntu, whenever the machine tries to start the GNOME Desktop Environment, it says it started it successfully. however, I never get a graphical desktop environment to use. I can fix this by logging into tty3 and typing gnome-session but I don't really want to do that as, for some reason, that skips login. Can anyone help? I want to pose a question such as:  What is your name? Joe  How would I accomplish this using Console.WriteLine to also wait for the response on that same line instead of it being broken into:  What is your name? Joe The sequence of triangular numbers is well known. Consider now the triangular numbers modulo some positive natural number $k$. That is, let $T_{n,k}$ be the remainder of dividing $T_n$ by $k$. For the regular sequence of triangular numbers, we can take as convention $T_n = T_{n, \infty}$.  Question: For all values of $k, i &lt; k$, does there exists some $n$ such that $T_{n, k} = i$ Minecraft extra folders? Once I click to run minecraft a small window appears saying "Downloading runtime", then three other folders appear onto my desktop: Game, Native Log, and Runtime. This really annoys me, as I have to keep deleting them after I am done with a session of minecraft. Why is this? It never use to happen before. Why use apparently meaningless do-while and if-else statements in macros? In many C/C++ macros I'm seeing the code of the macro wrapped in what seems like a meaningless do while loop.  Here are examples.  #define FOO(X) do { f(X); g(X); } while (0) #define FOO(X) if (1) { f(X); g(X); } else   I can't see what the do while is doing.  Why not just write this without it?  #define FOO(X) f(X); g(X) There are a lot of software in Windows to merge PDF files but how can we do the same in Ubuntu? Can I put 700c tires on rims made for 27 x 1.25"? If you cast Polymorph on a non beast creature then cast Awaken on their beast form how much carries over after polymorph ends?  Polymorph does not give any explicit information on what happens to your statistics when the polymorph ends:     The transformation lasts for the duration, or [drops to 0 hp]. [...] The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.  (Basic Rules, pg. 266)   So this leaves ambiguity when game statistics are altered during polymorph,   The charm effect of Awaken seems pretty clear from the  and reinforced by the specific wording referring to the target as a beast or plant during effects and a creature afterwards:     The awakened beast or plant is charmed by you [longer than polymorph.] When the charmed condition ends, the awakened creature chooses [...] (Basic Rules, pg. 216)   The other two effects of awakening (other than making a plant mobile) are less clear-cut:     The target gains an Intelligence of 10. The target also gains the ability to speak one language you know.  (Basic Rules, pg. 216)   I would guess the modification to intelligence would apply to the beast's stats and therefore end with polymorph.     as being independent of creature statistics and act more as the character's experience. I'd argue the experience of a stranger turning you into a mouse, then gifting you the ability - as a mouse - to speak a language you have never used before would be an experience you couldn't lose I'm not sure if the language and intelligence granted from awakening should remain linked.    These are two examples I can see this having significant impact on my campaign:   Meet an NPC I don't share a language with, Polymorph them then Awaken their beast form so they can speak my language. Can I now communicate with them when they turn back?  If their original intelligence was higher then 10 is it reduced to 10? Say I use find familiar to get an owl (classified as a fey) familiar, then polymorph it to an owl (classified as a beast) so my druid friend can cast Awaken on it, does my familiar keep an intelligence of 10 and/or the ability to speak?   So after reverting from an awoken polymorphed state would you keep the 10 intelligence and a new language, only the new language, or not keep either? How widespread is the practice of delegating LoR writing to the applicant? At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role.