Why toilet paper is softer in moist air? After a hot shower,the air from the bathroom is full of water steam,right?  How does the air affect the texture of the toilet paper?I mean,the toilet paper it seems to be softer,but why?  Can someone explain me,please?
Why is paper more frangible when it is wet? My four-year-old daughter asked me why paper tends to fall apart when wet, and I wasn't sure.  I speculated that the water lubricates the paper fibers so that they can untangle and separate more easily, but I really wasn't sure.
I need to find the cardinality of the set $S$ of all infinite subsets of $\mathbb{Q}$.   It's easy to prove $\operatorname{card} S=\mathfrak c$ if you first prove that the cardinality of the set of all finite subsets of $\mathbb{Q}$ is $\aleph_0$.   But is there some other proof for the statement without using the second one (about finite subsets)? Probably there is =) The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition Unfortunately hard disk of my system is damaged, now I recovered my database. But it cannot be attached again to SQL management studio 2005. The error is:  myfile.mdf is not a primary database file. (SQL server , error 5171) Why is foo.hasOwnProperty('__proto__') equal to false? Since i upgraded to Ubuntu 15.04, if i click on the shutdown button it only logs out and i have to click again on the shutdown button (from the ubuntu login screen) to power off the pc. How can i fix this? List sorting by custom field I dont know how to sort a list of SObject Case.  I have a List&lt;Case&gt; newCases which i iterate over in for cycle, where i save Cases to my new List&lt;Case&gt; casesList.  for (Case newCase : newCases) {             if(newCase.Case_Content__c == '111' &amp;&amp; newCase.Status == '24'){                 String cuid = newCase.CUID__c;                 cuidSet.add(cuid);                 casesList.add(newCase);                 casesList.sort(); //TODO sorting by CUID__c             }         }   What i need to do is, to sort this new list by field CUID__c. So the Cases with same CUID are together.  Thank you for any help :) Little Snitch reports outgoing connections for AirPlayXPCHelper for wrong subnets? After upgrading to El Capitan, I've started noticing annoying connections from the AirPlayXPCHelper to 192.168.1.0/24 subnet (my home network isn't in 192.168.1.0/24 subnet, it's in 172.16.0.0/12 subnet).  Questions are:   Why AirPlayXPCHelper goes out to this network on port 5000 and 7000? Is there a way to limit it's desire to go there?   Thank you. The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ is _____ I tried by taking the odd $n$ values as in that case, the integral I suppose was easier to calculate. So, denote $I_n=n\int_{0}^{1}e^{x^2}x^ndx$, then we have : $I_1=\frac{e-1}{2},\\I_3=\frac{3}{2},\\I_5=5(\frac{e}{2}-1),\\I_7=7(3-e)$ Then I tried calculating (random) values using calculator as integration was getting cumbersome. $I_{31}=2.488$, $I_{51}=2.57$. I do not see any kind of recurrence so that I can find a general term for odd $n$. I also tried the method given . The idea was that since integral doesn't depend on $n$ considering $I(n)=\int_{0}^{1}e^{x^2}x^ndx$, then $I'(n)=\int_{0}^{1}x^n\ln(x)e^{x^2}dx$, but this also doesn't lead me to any conclusion as well. I believe I couldn't get to a proper approach to tackle this question. Can someone please help with the idea that involves in solving these type of questions? While I was investigating a problem I had with lexical closures in Javascript code, I came along this problem in Python:  flist = []  for i in xrange(3):     def func(x): return x * i     flist.append(func)  for f in flist:     print f(2)   Note that this example mindfully avoids lambda. It prints "4 4 4", which is surprising. I'd expect "0 2 4".   This equivalent Perl code does it right:  my @flist = ();  foreach my $i (0 .. 2) {     push(@flist, sub {$i * $_[0]}); }  foreach my $f (@flist) {     print $f-&gt;(2), "\n"; }   "0 2 4" is printed.  Can you please explain the difference ?    Update:   The problem is not with i being global. This displays the same behavior:  flist = []  def outer():     for i in xrange(3):         def inner(x): return x * i         flist.append(inner)  outer() #~ print i   # commented because it causes an error  for f in flist:     print f(2)   As the commented line shows, i is unknown at that point. Still, it prints "4 4 4". How do I fix these M4 macro errors? I am trying to compile  but when I run ./autogen.sh the script terminates with these errors  Checking for required M4 macros...   libtool.m4 not found   glib-gettext.m4 not found   intltool.m4 not found   pkg.m4 not found   gtk-doc.m4 not found   yelp.m4 not found ***Error***: some autoconf macros required to build mate-desktop   were not found in your aclocal path, or some forbidden   macros were found.  Perhaps you need to adjust your   ACLOCAL_FLAGS?   What do I need to do to get rid of these errors? I tired installing the latest versions of inittool, glib, gtk, yelp, etc... but I still get the macros errors. Say an airplane flies at Mach 1. The doppler effect causes the front of the sound emitted by the plane to reach infinite frequency:    $f = \left ( \frac {343+0}{343-343} \right ) f_0 = ∞$  If the plane suddenly stopped, and there was an observer in front of the sound waves to receive the sound, what would the bunched up waves sound like to the observer? Would they cancel each other out and cause no sound? I've got a few macros that perform floating point lookups and calculations for me and I'm interesting in plotting their results. They're the kind of calculation which requires if/else, so they can't be easily written as a simple math formula for \addplot.  Thanks to a previous question (), I now know to use \pgfmathdeclarefunction, but after trying it I've found that addplot seems to prepend a "0Y" or "1Y" to values before passing them as function arguments. My external macros aren't prepared to handle this extra text, and I'm not sure why it's there.   In the course of testing things out, I've also found that calling a function defined with pgfmathdeclarefunction can also change the positioning of the graph...  \documentclass{article}  \usepackage{xparse}  \usepackage{pgfplots} \pgfplotsset{compat=1.10}  \begin{document}  % Example of a macro which does math outside of pgf     \ExplSyntaxOn     \DeclareExpandableDocumentCommand \doubleMacro { m }%      {%       \fp_eval:n { #1*2 }%Math performed by a package other than pgfplots      }%     \ExplSyntaxOff    %Demo: macro does work in regular text \doubleMacro{1.1}.  % Defining custom pgf functions for plotting      \pgfmathdeclarefunction{mathDoubleMacro}{1}{%         \pgfmathparse{\doubleMacro{#1}} %Calls macro which performs math done by another package     }      \pgfmathdeclarefunction{mathDoublePgf}{1}{%         \pgfmathparse{#1*2} %Uses pgf to do the same thing as an external macro could     }  %Generic plot with function given directly to \addplot \begin{center} \begin{tikzpicture}     \begin{axis}         \addplot[domain=0:1] {2*x};     \end{axis} \end{tikzpicture} \end{center}  %Plot using first macro: complains about 'Unknown fp word Y.' \begin{center} \begin{tikzpicture}     \begin{axis}         %\addplot[domain=0:1] {mathDoubleMacro(x)};%Commented out because it gives problems     \end{axis} \end{tikzpicture} \end{center}  %Plot using second macro: works, but graph is displaced to the right of the expected position \begin{center} \begin{tikzpicture}     \begin{axis}         \addplot[domain=0:1] {mathDoublePgf(x)};     \end{axis} \end{tikzpicture} \end{center}  \end{document}   If I define mathDoubleMacro as calling a non-existent macro, then the errors show which x-values which the addplot is trying to evaluate y at:    0Y0.0e0  1Y4.1666e-2 1Y8.3332e-2 ...  1Y9.9998401e-1   What are these nY's all about, and why does \addplot[domain=0:1] {mathDoublePgf(x)} give a graph with different positioning? There is a way to change top bar background opacity in ubuntu 20.04 lts.  I installed the hide top bar extension but is not a option to change it. We get a lot of questions on Super User about Windows activation and licensing. This question is an attempt to answer the most common questions in one place with a .   When reinstalling Windows, the following questions often come up:   Can I transfer the copy of Windows from my old computer to a new one? Does the license key on the sticker on my computer work on any computer? If I have a 32-bit version, can I install a 64-bit version? I have an OEM version of Windows, but only a retail disk. Can I still use it? I want to install Windows with a different language. Do I need a new license in that language? I changed some hardware. Will I be able to reactivate my computer? Can I back up my activation before doing a reinstall? How many computers can I install my license on? Do I have to deactivate my old installation before transferring a license? If so, how? How does licensing work in Windows ? What are the restrictions on transferring, reinstalling, and changing versions of Windows? Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd.   My attempt: If $a$ is even, let $a = 2^{s}k$ for some integers $k, s$ Then, $$a^{2^{n}} + 1 = 2^{2^{n}s}\cdot k^{2^n} + 1$$ and $$a^{2^{m}}  + 1 = 2^{2^{m}s}\cdot k^{2^m} + 1$$ To prove that they're relatively prime, we need to show that their gcd = 1. And I was stuck here, how could I prove that gcd of two numbers is $1$?     A hint would be sufficient. Thanks. Why do damaged hard drives freeze the entire system? Is it legal to add your publications to ResearchGate? I recently created a profile on . And to add your publications list it requires you to upload the paper. Is it legal to upload published journal articles on public servers, where everyone can download it for free? If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis Why is rm allowed to delete a file under ownership of a different user? From the post  I understand that rm just needs write permission on directory to remove the file. But I find it hard to digest the behaviour where we can easily delete a file who owner and group different.  I tried the following  mtk : my username abc : created a new user  $ ls -l file -rw-rw-r-- 1 mtk mtk       0 Aug 31 15:40 file $ sudo chown abc file $ sudo chgrp abc file $ ls -l file -rw-rw-r-- 1 abc abc       0 Aug 31 15:40 file $ rm file $ ls -l file &lt;deleted&gt;   I was thinking this shouldn't have been allowed. A user should be able to delete only files under his ownership? Can someone shed light on why this is permitted? and what is the way to avoid this? I can think only restricting the write permission of the parent directory to dis-allow surprised deletes of file. Viewing computer screen through 3D glasses, why the asymmetry?