Why can't regex find letters inside words?
What is the difference between re.search and re.match?
How is an empty set truly "empty"? In a  question, an answerer says:  an empty bag is a bag with nothing inside it.  Makes sense, but I'm reading a textbook right now that says:  The empty set has only one subset (namely, itself).  Which seems odd to me. If a set is empty, why would it contain a subset? Regardless of whether or not the subset is also an empty set, the &quot;empty set&quot; still contains a subset, so how is it really &quot;empty&quot;? To go back to the empty bag analogy, it just sounds like my text book is saying:  an empty bag is a bag with nothing but an empty bag inside it.  Which doesn't make sense because then the bag isn't empty. I can't wrap my head around this concept. Firstly, this is a homework problem so please do not just give an answer away. Hints and suggestions are really all I'm looking for.  I must prove the following using mathematical induction:     For all $n\in\mathbb{Z^+}$, $1+2+2^2+2^3+\cdots+2^n=2^{n+1}-1$.   This is what I have in my proof so far:     Proof: Let $p\left(n\right)$ be $\sum_{j=0}^n 2^j=1+2+2^2+\cdots+2^n=2^{n+1}-1$. Then $P\left(0\right)$ is    \begin{align} \sum\limits_{j=0}^0 2^j=1=2^1-1.\tag{1} \end{align} Hence    $P\left(0\right)$ is true. Next, for some $k\in\mathbb{Z^+}$, assume    $P\left(k\right)$ is true. Then \begin{align}  \sum\limits_{j=0}^{k+1}2^j&amp;=\left(\sum\limits_{j=0}^k  2^j\right)+2^{k+1}\tag{2}\\ &amp;=2^{k+1}-1+2^{k+1}\tag{3} \\ &amp;=2\cdot 2^{k+1}-1\tag{4}\\ &amp;=2^{k+2}-1\tag{5}\\ &amp;=2^{\left(k+1\right)+1}-1.\tag{6} \end{align}   Therefore, $P\left(n\right)$ holds for all $n$.$\;\;\;\;\blacksquare$   Is everything right? My professor went over the methodology in class quite fast (and I had a bit too much coffee that night) and I want to make sure I have it down for tomorrow night's exam. Compiling PHP 5.1.6 with PDO MySQL Replace arbitrary characters in the middle of an IP address string with sed I need to find and replace either one or two numerical characters in strings in a file.  The strings are IP addresses of the form:   10.xx.y.z    Where xx can be one or two characters.    I want to replace the xx with the single character 0, so I have  10.0.y.z    preserving the values of y and z.   The string may appear multiple times in the file.  What is the sed invocation to do this? Benefits of Toad houses I have a few red Toads and a Toad is just hanging out in town. I see an option to buy a red Toad house, ostensibly for him. Are there any added benefits of purchasing this or are the colored Toad houses just cosmetic? How to turn off chrome's annoying auto-fill? LaTeX Classes or Styles for Schedules and/or Calendars? Adapt BibTeX style to give all initials I'm using a modification of the plainyr BibTeX style. Although my bib-file contains all initials for some authors (e.g. B.D. McKay), I end up with just the first initial in my document (e.g. B. McKay). I thought about editing the BibTeX style myself, but after seeing the code, I decided against it. Maybe there are some people who are more knowledgeable in this area of expertise.  I want my final document to include the initials for all the names, and not just those of the first name.  This is the relevant code of the BibTeX style, or at least, I think it is the relevant code.  FUNCTION {format.names} { 's :=   #1 'nameptr :=   s num.names$ 'numnames :=   numnames 'namesleft :=     { namesleft #0 &gt; }     { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=       nameptr #1 &gt;         { namesleft #1 &gt;             { ", " * t * }             { numnames #2 &gt;                 { "," * }                 'skip$               if$               t "others" =                 { " et~al." * }                 { " and " * t * }               if$             }           if$         }         't       if$       nameptr #1 + 'nameptr :=       namesleft #1 - 'namesleft :=     }   while$ } Within a custom command, I'm doing the following to write to a file:  \newcommand\mycommand[1]{   \newwrite\file   \immediate\openout\file=foobar.tex   \immediate\write\file{     foo     bar     #1     blarg   }   \immediate\closeout\file }   Of course when I invoke it as \mycommand{baz}, I get the following contents in foobar.tex:  foo bar baz blarg   with all new lines turned into spaces by LaTeX. My question is, is there a way to output these lines into the file "as expected", i.e. with real new lines at the end of each line instead of a space? I'm thinking some \catcode wizardry should do the trick, but I'm not sure which character I need to redefine and to what category code.  Update  The solution in  works perfectly. The only problem is when #1 contains embedded newlines. I can of course send it to mycommand with its own slew of ^^J, I was wondering if there is a way to avoid this. I've set up the physics of a swinging wrecking ball and set the animation to run for 240 frames.  This was not long enough for the entire "swing" of the ball-and-chain.   I'm unable to reset the timeline, but I can set the end frame to (say) 1000 frames, but when I try to play the animation, the animation progress halts at frame 240 and I cannot get it to go any further.   There are no markers or keyframes in the timeline.  What should I do to "force reset" the animation-timeline, to allow changes to the length? Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ Let IG denote Inverse-Gamma distribution   .   If $X\sim IG(\alpha,1)$ and $Y\sim IG(\beta,1)$. Show that   $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$   I tried with jacobian transformation taking $Z=\frac{X}{X+Y}$ and $W=Y$ then $$X=\frac{WZ}{1-Z};Y=W$$  $$\frac{\partial(z,w)}{\partial(x,y)}=\frac{1}{(1-z)^2}$$  $$f_{z,w}(z,w)=f_x(\frac{wz}{1-z})f_y(w)(1-z)^2$$ $$f_{z,w}(z,w)=\frac{1}{\Gamma{(a)}}(\frac{wz}{1-z})^{-\alpha-1}e^{-\frac{(1-z)}{wz}}\frac{1}{\Gamma{(\beta)}}w^{-\beta-1}e^{-\frac{1}{w}}(1-z)^2$$  but I'm stuck, in some place I read that $\frac{X}{X+Y}$ is a type 3 Beta distribution, but I can't show that. Whenever I'm trying to close a file that has been changed, I get the save file dialog    I remember that the Don't Save button used to have focus, so I could press it using Spacebar, while pressing Enter would click on Save. But now on Lion, I'm unable to find a way to press the Don't Save using keyboard only, since Tab doesn't change focus to anything, and space doesn't work either.  This is the same for all file save dialogs in the system. Is there any way I can press the Don't Save button using keyboard only? Terminal not displaying colors for directory listings I don't know why my bash session doesn't show colors. I have tried Terminal as well as iTerm.  I have tried:   ls -G Setting export CLICOLOR=1 and export LSCOLORS=GxFxCxDxBxegedabagaced Using different themes such as solarized and something else   The versions of my software are:   bash: GNU bash, version 3.2.51(1)-release (x86_64-apple-darwin13) osx: 10.9.2   I have Homebrew installed  I don't know what other information might be helpful. I spend a lot of time on the shell, this problem is becoming very annoying :)  edit: in terminal preferences, I have 'Declare terminal as: xterm-256color' and 'Display ANSI colors' along with 'Use bright colors for bold text' I'm trying to typeset a table that would have a header in the first row (I'm not looking for a different/better solution to adding a header, but for a fix to this solution. Thanks). I want to achieve this by having a multicolumn cell spanning all the columns of the first row. The problem is that if the text is too long, the column widths are uneven, with the last column accumulating excess width. I would expect all of the columns to be of approximately the same width (although I cannot find a decent source that would say they should), given the fact that all the text in the second row is of approximately the same width.  I find this behaviour quite puzzling and have no idea what the cause could be. I know I could perhaps remedy this by manually setting the column widths, but am curious as to how to fix this without doing that (I do not need or indeed want the columns to be of the same width, but roughly proportional to the length of their content), preferably but not necessarily by using the tabular environment only (some other conflict with the document class I am using).   What is it that I'm doing or assuming wrong? And why?  MWE:  \documentclass{article} \begin{document}  \begin{tabular}{ccccc} \multicolumn{5}{c}{This is a piece of text. The longer it is, the longer the last column.} \\  1 &amp; 2 &amp; 3 &amp; 4 &amp; 5 \\ \hline \end{tabular}  \end{document}   Resulting table. Notice how the last column of the second row accumulates excess width. Is it possible to play D&D 5e solo? Is it at all possible to run a solo game where you act as the DM/GM for yourself? I know there was a 4th edition adventure published in an old issue of one of the D&amp;D magazines but recently I read somewhere (Reddit I think) that the games Outbreak: Undead and Eclipse phase were good games to play solo.  Can anyone with experience with running a game of D&amp;D 5e for themselves explain how to do so? How can I vertically align the numerators of two fractions? In languages like Java and C#, strings are immutable and it can be computationally expensive to build a string one character at a time.  In said languages, there are library classes to reduce this cost such as C# System.Text.StringBuilder and Java java.lang.StringBuilder.  Does php (4 or 5; I'm interested in both) share this limitation?  If so, are there similar solutions to the problem available? The only place I am aware of is the . How would I use Takeown to take ownership of all folders on one drive? Windows 8 opens notepad on boot- no startup entry found I just upgraded from windows 7 to windows 8 and everything is working fine except notepad keeps opening on boot with a "access denied" window that comes up as well. I've ran MBAM and removed some junk, I've disabled every "file not found" item in autoruns as well as something that had a text/xml title in it and I've ran CCleaner a few times. Nothing is working, any help is much appreciated!