Is strict cardinality ordering preserved by power sets?
Do sets, whose power sets have the same cardinality, have the same cardinality?
Can a Rogue (D&D 3.5) use sneak attack on both the first and second attack? I know this seems like a question you can simply Google but the answers vary and my clan is under the impression that I can only use it on my first attack (once per round) and not on my second attack.  From Googling, I've understood that as long as the monster / enemy is flat-footed, flanked or caught off-guard, I can apply sneak attack on both my first and second attack in a round.  Is this correct?  Is it normal if the clan simply decides that that gives me an unfair advantage in combat and gives me only one sneak attack per round? How to Configure Launcher Placement in Multi-monitor Setup I use a large monitor as primary and laptop screen as secondary. Is it possible to move the launcher to my big monitor or do I have to turn off my laptop monitor?   "Monitor Preferences" (Launcher search -> "Monitors") does not have a way to set the default/primary monitor. nvidia-settings which I just installed says "You do not appear to be using the NVDIA X driver. Please edit your X configuration file (just run nvidia-xconfig as root), and restart the X server.  sudo nvidia-xconfig says sudo: nvidia-xconfig: command not found.  I guess I don't have an AMD driver because I don't have "AMD Catylist Control Center" in the launcher search. Which are the non Schengen countries that allow entry for Schengen visa holders? There are countries in the Balkan area that allow entry if you have a Schengen visa but am not able find a definite list of all those countries. Knowing that will save me getting a visa for all those countries when I do my mega Euro trip. Pretty much the problem asks if a function is continuous at the point $c$ and $f(c) &gt; 0$ then there exists a $d &gt; 0$ such that $\forall x$, $f(x) &gt; 0$ with $|x-c| &lt; d$.   I can understand what the problem means. That if a function is positive at a point then there is another point that's really close that'll also be positive. I can not prove this in a formal way though. I've tried using the intermediate value theorem and I do not know hot to implement it. Any ideas? Inverse Fourier transform of Gaussian I need to calculate the Inverse Fourier Transform of this Gaussian function:  $\frac{1}{\sqrt{2\pi}} exp(\frac{-k^2 \sigma^2}{2})$  where $\sigma &gt; 0$, namely I have to calculate the following integral: $\int{\frac{1}{\sqrt{2\pi}} \exp(\frac{-k^2 \sigma^2}{2})} \exp(ikx) dk$.  How can I do that? If I am not wrong (in which case please correct me) the result should be $\frac{1}{\sqrt{2\pi}\sigma}exp(\frac{-x^2}{2\sigma^2})$...but I don't know how to get there! Why doesn't the frequency of light change during refraction? When light passes from one medium to another its velocity and wavelength change. Why doesn't frequency change in this phenomenon? I'm using Bash on both client and server. When running a command over SSH:   ssh &lt;host&gt; 'declare' gives a list of shell variables. ssh &lt;host&gt; 'mount' gives a list of mountpoints.   However, declare is a Bash builtin, while mount is an external command. How does SSH know which to run if there is a shell builtin and an external command with the same name on the server? Encountered an error while updating through Synaptic Manager. Subsequent updates gave the error at the bottom of the output. I'm a noob so any help is appreciated.  al@al:~$ sudo apt-get -f upgrade Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following NEW packages will be installed:   libjack-jackd2-0:i386 The following packages have been kept back:   linux-headers-generic skype 0 upgraded, 1 newly installed, 0 to remove and 2 not upgraded. Need to get 0 B/202 kB of archives. After this operation, 493 kB of additional disk space will be used. Do you want to continue [Y/n]? y (Reading database ... 310056 files and directories currently installed.) Unpacking libjack-jackd2-0:i386 (from .../libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb) ... dpkg: error processing /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb (--unpack):  './usr/share/doc/libjack-jackd2-0/buildinfo.gz' is different from the same file on the system dpkg-deb: error: subprocess paste was killed by signal (Broken pipe) Errors were encountered while processing:  /var/cache/apt/archives/libjack-jackd2-0_1.9.8~dfsg.2-1precise1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1) Electric fields in continuous charge distribution My question may be very basic, but I can't think of a reasonable explanation for this.  Consider a solid charged sphere. Now, we have an electric field inside the solid sphere, but at any particular point there are charges infinitesimally close to the point. As I see it, these charges should contribute to an infinite value of the electric field.  One might possibly argue that at any given point, infinitely-close charges are distributed uniformly everywhere and hence their effects cancel out. But at the surface of the sphere the uniformity of infinitely-close charges is not present and hence here we must have infinite field, but that is not the case as well! Where are we going wrong?  Also, if we think of electric field at that point in continuous charge distribution, the contribution of electric field might exist finitely from nearby charges with both charge and distance between them tending to zero, but for the very small charge present exactly there, the electric field contribution from itself must be infinite with charge being finitely small and distance being exactly 0. What's wrong here?  I have strong suspicions, is it sensible and correct to define electric fields at such a close vicinity of other continuous charges? What exactly do \csname and \endcsname do? What exactly do \csname and \endcsname do? What are their job? I have glanced at the Texbook and some other books, but none of them was clear enough to me. Can anyone please give a simple example to clarify this issue? When we want to open an application or file from the terminal, we type, say,  okular file.dvi   This opens the application, but also shows the status of the application. We cannot close the terminal, because it kills the process. Unfortunately, if you're trying to, for example, create a LaTeX file, you will need one tab for the text editor, one for the dvi file, and so on. And if you're trying to open all windows from the terminal, you can forget it. I'm trying use the terminal as much as possible, and while I have Yakuake, it is still a bother having so many tabs and seeing which of those have an application I've killed and so on.  So, is there a way to open an application/file from the terminal so that the status doesn't show and immediately gives the prompt so that we can use it to open more applications? Find all $x$ such that $x^6 = (x+1)^6$. Find all $x$ such that $$x^6=(x+1)^6.$$   So far, I have found the real solution $x= -\frac{1}{2}$, and the complex solution $x = -\sqrt[3]{-1}$.  Are there more, and if so what/how would be the most efficient find all the solutions to this problem? I am struggling to find the rest of the solutions. Money from my parents from abroad to my bank account in UK I am from Japan. I have moved to UK recently on a spouse visa.   I still have my Japanese bank account which I have been using even before I came to UK. I have saving in that account and also my parents transfer me some money per month in my bank account in Japan. I have an International Debit Card on this account.  I am withdrawing this Money in UK via ATM / Debit Card.  In this case, do I have to pay taxes in UK or declare this as income in some form. Making separate Python installation that can call ArcPy? Did merging Black Holes in GW150914 give up entropy and information to the gravitational waves, since they lost 3 solar masses? Since the final Black Hole (BH) had 3 solar masses less of mass than the original binary BH, it seems the 2 BHs lost mass, and with it event surface area, entropy, and information. If that came from inside the BHs it seems that it would be a contradiction of what a BH is --'nothing escapes its event horizon'. Some may say that came from the rotational energy of the pair, but the new BH now seems to have less than the two original ones summed. So, did some of that escape the horizons? Print programs with its proper syntax I have defined my own language whose syntax is very close to the one of Pascal. I would like to type the following program for instance. Many people use the packages algorithmicx or algorithm2e to print programs, but it seems that we have to use their specific keywords of its syntax like procedure, end while.  I just want to indent spaces when needed, and bold some words when I want (sorry that I could not bold letters in the following figure). Do I have to use  texttt for each line? Also, with verbatim, I could not bold words...  Also, as the program is not large, I would need to put it on the left side of the page, and leave space for some explanasion text on its right hand side. So I  guss I need to get them all together, and use multicols.  Could anyone help?  program test                                      some text here var   i : integer;                                    ...    b : boolean; begin    i := 1;                                        ...    b := true;    while i &lt; 15 do       i := i  + 1;       b := not b                                  some text here    od end   Edit1: Following @Werner's tabbing solution, I have made the code a minipage:  \begin{minipage}[t]{0.48\linewidth}% \begin{tabbing} Werner's solution \end{tabbing} \end{minipage}\hfill \begin{minipage}[t]{0.48\linewidth} a paragraph \end{minipage}   Actually as the code shows, I want the texts to be another separated minipage on the right hand side of the code. I have then 2 questions:   is it reasonable to make 0.48\linewidth instead of 0.5\linewidth? 0.48\linewidth is a conventional choice? is it possible to make a frame around the code, and use \caption and \label to make it a reference (I prefer figures)? shopt works in command line, not found when run in a script I'm writing a script to copy some files around, and trying to use shopt -s dotglob  like .jshint and whatnot.    I can run shopt -s dotglob directly at a bash prompt with no error.  However, running the script throws the error:  script.sh: 81: script.sh: shopt: not found   I'm running this script in bash shell, with the shebang header #!/usr/bin/env bash.  Error line:  shopt -s dotglob cp -r $TEMP/img/* $TARGET/img/ cp -r $TEMP/js/* $TARGET/js/ cp -r $TEMP/less/* $TARGET/less/   Not finding anything helpful on google, any idea what the problem is here? Reducing voltage with resistors How can I determine accuracy of past probability calculations? I do not study statistics but engineering, but this is a statistics question, and I hope you can lead me to what I need to learn to solve this problem.    I have this situation where I calculate probabilities of 1000's of things happening in like 30 days.  If in 30 days I see what actually happened, how can I test to see how accurately I predicted?  These calculations result in probabilities and in actual values (ft).  What is the method for doing this? Thanks, CP I'm looking for a phrase that describes trying to fix problems caused by underlying issues, with the result of compounding the issue. I usually call this "targeting surface problems rather than root problems", but my terminology is verbose.  Example 1: A government bans buying and selling bananas in the state. Later, it passes a clause allowing citizens to purchase imported bananas.  Example 2: A divided highway is erected with two lanes going in each direction but, since it gets lots of traffic, the shoulders are widened into new lanes. This leaves no shoulder room.  What would be a more concise phrase?