b) How many onto functions are there from A to C?
Number of onto functions
How do you allocate more RAM to Minecraft? There is a lot of lag when I play Minecraft. I think this is due to the low amount of RAM I've allocated to Minecraft. (495MB)  How do you allocate more RAM to Minecraft?  I checked my other computer (Intel i5 Core) and it had the same amount of RAM allocated to Minecraft. However, Minecraft did not lag on that computer.  After I installed Optifine on this computer, the lag stopped (I don't know why cause I read that Optifine splits the load onto 2 cores, but I have only one core (At least I think so, a sticker on the laptop says Intel CORE i7)). I'm trying to delete a folder in Windows 7 and get a perplexing error message: "Could not find this item:  This is no longer located in G:\Graphics.  Verify the item's location and try again.  I can see the folder -- I can find it.  I just can't delete it.    I also get a second error message (sometimes) when I click on the folder: G:\Graphics 2009-11-17 refers to a location that is unavailable...this information might have been moved to a different location.    I'm using Windows 7; this folder is on an external hard drive.  I've emptied the folder (there were items in it); I've scanned that external hard drive for errors.  Trying to rename the folder yields the same enigmatic error message.    Is there a way to delete this folder? I am trying to find and replace the * (star, or shift+8) character in a bunch of formulas in Excel 2007.  * of course matches the ENTIRE contents of the cell, which is not what I want.  How do I disable this behavior? How to change "to" to "-" while displaying start and end date in views? How can I produce a 'ring (or wheel) chart' like that on page 88 of the PGF manual? Has there ever been a warp / non-warp collision? Like something going at warp hits a planet, star, another ship, moon, satellite, alien, tribble, etc.... Basically, can stuff in subspace (warped stuff) hit stuff in real space (not warp)?  Star Trek: The Voyage Home shows us clearly that entering warp speed within Earth's atmosphere has no adverse consequences for the starship or the environment.  HMS Bounty went through miles of atmosphere, dust, birds, and clouds and nothing entered  to hit her. Enterprise did this again by dropping out of warp in Titan's atmosphere.  which explains some tech used, but now we have to ask if there is even a hazard of collision at warp. Has there ever been a collision in the franchise - any normal object being hit at warp speed? (This obviously doesn't include things traveling at warp together, like photon torpedoes from one ship to another).  Closest example I found: In  Enterprise attempts warp before balancing their warp drives and creates a wormhole instead. They nearly collide with an asteroid which was already inside the wormhole, but neither the ship not the asteroid were traveling at warp.  Compressing Space Real-world (non-canon) attempts to explain ST warp technology rely on compressing space itself in front of the vessel. The image sequence below from Star Trek: Into Darkness (canon) shows Enterprise warping past the USS Vengeance and confirms that Enterprise actually gets smaller (or compresses the space around it). The light on Vengeance shows that at the instant the two ships are side-by-side Enterprise looks like a toy beside it. (Large image needed for detail - sorry):    Thus objects at warp occupy less real space - possibly none at - because , which according to Memory-Alpha is implied to be the medium which FTL travel happens. Normally subspace and real space do not interact. When they do it is called a .  Also, objects inside the warp bubble are not moved by the warp drive:     The observer(spaceship) is still immersed in the interior of the warp bubble and this bubble is carried   out by the spacetime ”stream” at faster than light velocities with the observer at the rest with respect to   its local neighborhoods  (p. 25)   It is my belief that to be consistent with warp bubble physics derived from the Einstein Field Equations in general relativity, the ST interpretation of warp speed travel should not allow collisions between n-space objects and objects within a warp bubble and remove the phenomenon from any plotlines such that warp travel is intrinsically safe for the traveller, but possibly greatly impactful for the normal world outside.  But has it happened?  Points of clarification raised by comments  Deflector Shields: Yes, ships have them. Gene Roddenberry envisioned Navigational Shields which would deflect anything in front of the ship, from a single hydrogen atom to an asteroid (see his notes below).    It's important to note that much of what he had in this guide was changed in final production. In fact, based on this guide we could write an entire episode on a simple deflector sabotage resulting in them hitting a hydrogen atom. Real science calculations tell us that even hitting a photon of light would release incalculable energy.  These notes very much explain the many questions asking why ships don't go to warp inside a solar system. Solar systems are FULL of particles and debris, which would require a great deal of energy to deflect. Interstellar space simply draws less power because the shields work less. Convert NTFS to FAT32 without losing data I understand that you can  without formatting or backing up the data and later restoring - is the same thing possible in the other direction?  I want to convert my NTFS portable hard drive to FAT32 so that my PS3 will recognise it.  If it's not possible from within Windows, are there any free programs which will allow me to do it? Inequality between $\ell^p$-norms Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$? Let $a$ be a non-zero real number. Is it true that the value of $$\int\limits_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$$  is independent on $a$? Remove all packages installed from a PPA? I have installed LibreOffice 4 using PPA. I was using LibreOffice 3, then  I had upgraded to LibreOffice 4, because I was somewhat eager to try a new version.   Now since I found that LibreOffice 4 has some issues, including handling my native language, I want to move back to LibreOffice 3.  This question  has already some answers which has some similarity with my above mentioned issue, but it does not solve my problem. This question talks about downgrading from a specific version of LibreOffice, namely from 4.0 to 3.6. The solutions mentioned are not the ones I am looking for. They will work, but the  solutions suggest either downloading .deb files for LibreOffice 3.6 or adding PPA for them. Furthermore, some of the answers put out-of-proportion~(applicable for the solution, however) stress on use of , not general command-line-solution.     I want a general solution without using PPA or downloading .deb files. All I want is to move back from the (higher) PPA version to the (lower) official version.  Anyway, in order to accomplish this, I removed the LibreOffice config directory from my home and then purged LibreOffice from my machine.  sudo apt-get purge libreoffice-*   Then I removed the relevant PPA's using the sudo apt-add-repository --remove command. And then ran sudo apt-get update.  Now, when I try to install LibreOffice using the command  sudo apt-get install libreoffice   I get an avalanche of output about unmet dependencies, something like,   The following packages have unmet dependencies:  libreoffice : Depends: libreoffice-core (= 1:3.5.7-0ubuntu4) but it is not going to be installed (snipped)    If I dig the issue further, by using the command,  sudo apt-get install libreoffice-core   I get    The following packages have unmet dependencies:  libreoffice-core : Depends: libreoffice-common (&gt; 1:3.5.7) but it is not going to be installed                 Depends: libexttextcat0 (&gt;= 2.2-8) but it is not going to be installed                 Depends: ure (&gt;= 3.5.7~) but it is not going to be installed E: Unable to correct problems, you have held broken packages.    Could you please tell me how do I install LibreOffice 3 in my machine?  I am using Ubuntu 12.04 LTS.    EDIT  Before receiving , I was wondering, at this very moment, if I take a fresh computer, and install Ubuntu 12.04, LibreOffice installation will work without a hitch. Then why I can not install LibreOffice in my 12.04 machine today from simple command line?  Then the accepted answer clarified everything. I need to use ppa-purge so that this resets all packages from a PPA to the standard versions released for my distribution.  Basically it is like a way to restore my system back to the way it was before my installed packages from a PPA.  further elaborates the idea.    worked perfectly for me. Actually, this was an education for me since it taught me how do downgrade a package that was added via PPA. And I realized that the answer actually teaches us to "move from PPA installation  of a package to official lower version package." Iterating each character in a string using Python In C++, I can iterate over an std::string like this:  std::string str = "Hello World!";  for (int i = 0; i &lt; str.length(); ++i) {     std::cout &lt;&lt; str[i] &lt;&lt; std::endl; }   How do I iterate over a string in Python? combinatorics circular arrangement problem If $n$ distinct things are arranged in a circle, then what are the number of ways selecting three of these things so that no two of them are next to each other? How do we solve (i.e. get the closed form of) $\int \sqrt{1 + t^2} dt$ ?   shows the closed form of it but not the steps in solving it.  I think I need some algebraic trick..   I thought of some hyperbolic functions and their derivatives and equalities:  If I make $ t = \sinh x$, then I can reduce the integral to  $$ \int \cosh ^2 x dx $$ though I'm not sure if this is valid. But from here, I cannot go on evaluating the integral... Travel on a Schengen visa stating EEA family member without spouse? How can I serialize an object to JSON in JavaScript? "Unable to locate package" while trying to install packages with APT When I try to install any package through the command line, I get an error.   $ sudo apt-get install &lt;package&gt; Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package &lt;package&gt;   Can anyone help me on this? I use the babel package in order to write in greek with font "kerkis".  I want to add code in english ("courier new" font) to my latex document but I get some difficulties.  Can anybody help me, please. Thank you in advance.  \documentclass[12pt]{article} \usepackage[english,greek]{babel} \usepackage[utf8x]{inputenc} \usepackage{graphicx} \usepackage{fancybox} \usepackage{verbatim} \usepackage{courier} \usepackage{kerkis} \usepackage{float} \usepackage{geometry} \usepackage{fancyhdr} \usepackage{titlesec} \usepackage{tocloft} \usepackage{hyperref} \usepackage{afterpage} \usepackage{color}    \usepackage{listings}  \renewcommand{\lstlistingname}{Κώδικας}  \lstset{  %matlab   backgroundcolor=\color{white},     basicstyle=\normalsize,    % COURIER NEW?        commentstyle=\color{green},    % comment style   escapeinside={\%*}{*)},           extendedchars=true,               frame=single,                              keywordstyle=\color{blue},       % keyword style   numbers=left,                     numbersep=5pt,                     numberstyle=\normalsize\color{black},    rulecolor=\color{black},           stepnumber=1,                      stringstyle=\color{magenta},     % string style }   \begin{document}  \selectlanguage{greek} Ελληνικά: \textlatin{this word means greek}  \selectlanguage{english} Now I write in english  \selectlanguage{greek} Ελληνικά  %\selectlanguage{english}???  \begin{lstlisting}[caption = \textlatin{example1.m}] { % Entropy E = 0; for i = 1:J     if p(i) ~= 0         E = E + p(i)*log2(1/p(i));     end end } \end{lstlisting}  \end{document} I've seen a couple questions around here like , which mentions:     Unfortunately that same browser won't allow me to test HTTP PUT, DELETE, and to a certain degree even HTTP POST.   I've also heard that browsers support only GET and POST, from some other sources like:        However, a few quick tests in Firefox show that sending PUT and DELETE requests works as expected -- the XMLHttpRequest completes successfully, and the request shows up in the server logs with the right method. Is there some aspect to this I'm missing, such as cross-browser compatibility or non-obvious limitations? $ not defined using jQuery in WordPress Determine the number of functions $f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd. Problems:Determine the number of functions $$f: \{1,2,3....,1999\}\to \{2000,2001,2002,2003\}$$ satisfying the condition that $f(1)+f(2)+...f(1999)$ is odd.   My Attempt: Each integer in domain has $4$ choices and therefore the total number of functions is $f$ is $4^{1999}.$ Since there are an equal number of functions that yield odd or even result, we can directly write that the number of functions satisfying the above condition to be $2*4^{1998}.$ I am unsure about this last claim and would like to prove it (if it is true.)Also is the answer to this problem correct?  Edit $1$: I tried to proceed further in the following manner:   For a given mapping $f$ let the number of integers assigned to $2000,2001,2002$ amd $2003$ be $p,q,r$ and $s$ respectively, where $p,q,r,s\in \mathbb{Z}^+$. Therefore the sum in question can be written as $f(1)+f(2)+...+f(1999)=2000p+2001q+2002r+2003s.$ Clearly the sum will be odd iff $q+s$  is odd. Also note that $p+q+r+s=1999\Rightarrow p+r$ is even. On the other hand if we let $q+s$ as even then $p+r$ must be even. Now the number of values of $p,q,r$ and $s$ for which the above two lemmas hold is the same and therefore if we let $f$ to be the function which maps elements form $\{1,2,3,...,1999\}$ to $\{2000,2001,2002,2003\}$ such that $q+s$ is even and $g$ to be the function  hich maps elements form $\{1,2,3,...,1999\}$ to $\{2000,2001,2002,2003\}$ such that $p+q$ is even we will get a bijection.(Maybe!)