I'm working with matrices in R, and noticed something strange:  set.seed(1234) m &lt;- replicate(10, rnorm(20)) all(m / 7 == m * (1/7)) #FALSE   Why is that ? Shouldn't the multiplication by the reciprocal be equivalent to normal division ?
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
Transit Visa for Thailand Im an Indian citizen. Do I need a transit visa in Thailand while going to Angkor Wat from Kolkata (India), and can I stay in Thailand for two days on this transit visa? Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$ $\sum_{n=1}^\infty n*(n+1)*x^n$  Hello everyone,  I need help in solving the question above.  I started with $\frac{1}{1-x} = \sum_{n=0}^\infty x^n$, if differentiated it once so it became $\frac{1}{(1-x)^2} =\sum_{n=1}^\infty nx^{n-1} $ but from here I don't know how to continue. Thanks. What would be the quickest way to construct a Python binding to a C or C++ library?  (I am using Windows if this matters.) Using Newton's Law of Universal Gravitation to find distance, with the question not giving sufficient information to substitute into the equation. Problem:  $F = \frac{(G m_1 m_2)}{r^2}$  An object of unknown mass is placed directly between the Earth and the Moon such that the forces of gravity acting on the object are equal from both the Earth and the Moon. The distance from the Moon to the object is exactly one-tenth of the distance from the Moon to Earth. Using the above formula, determine the distance from the Moon to the Earth.  Given is:  The factor $G≈6.67∙10−11\mathbf{N(\frac{m^2}{kg^2})}$ is a universal constant.  Mass of Earth $≈5.972∙10^{24}\mathbf{kg}$   Mass of the Moon as $≈7.348∙10^{22}\mathbf{kg}$  Mass of unknown object = $m$  My solution:  $F = \frac{(6.67 *10^-11) m (7.348*10^{24})}{R^2}$  $F = \frac{(6.67 *10^-11) (5.92* 10^22) m}{10R^2}$  As gravitational force acting on the object is equal   $\frac{(5.92\cdot 10^22)}{100r^2} = \frac{(7.348*10^{24})}{r^2}$  $R = 1.24 \cdot 10^4 KM$  Is this a viable solution to the problem? Please provide feedback. Thank you! I get this message while trying to install Ubuntu 12.04 as a guest in VirutalBox 4.1.18, on an Ubuntu 10.04 host.         This kernel requires the following feature not present on the CPU: pae   Some host specs:     The host's kernel is: Linux 2.6.32-41-generic-pae GNU/Linux   lscpu (host): Architecture: i686, CPU op-mode(s): 32-bit, 64-bit   grep --color=always -i PAE /proc/cpuinfo   does show pae in its output.   The 12.04 iso used is: ubuntu-12.04.0-desktop-i386.iso      As a comparison/check, I downloaded and installed Linux Mint 13 Cinnamon to the same host on the exact same VM (I just changed the .iso image). It worked fine. Its iso is: linuxmint-13-cinnamon-dvd-32bit.iso   It seems (to me) that I have pae.. what is going on here?   Update: I had assumed that Linux Mint also required pae (being Ubuntu based), but I've just run;   grep --color=always -i PAE /proc/cpuinfo   in the Mint VM.   It showed no output.   So it seems the issue may lie with VirtualBox.   If that is the case, how can I get Virtualbox into pae mode? I know that packages installed with apt-get are stored in /var/cache/apt/archives.  I just installed mariadb server in Ubuntu 16.04 with following command:  sudo apt install mariadb-server   When I tried to find packages in /var/cache/apt/archives, there are no packages. Where are they stored if it's not in this directory? Formatting Ticks and FrameTicks labels with a function How do I run two isolated instances of firefox? How can I install Whatsapp web app on Ubuntu? I found a similar question , but here I am asking for the WhatsApp desktop webapp so that I can directly access the application without opening a browser. Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective Let $f: A \rightarrow B$ be a function. How can we show that for all subsets $S$ of $A$, $S \subseteq f^{-1}(f(S))$? I think this is a pretty simple problem but I'm new to this so I'm confused.  Also, how can we show that $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective? Lost my old passport for Schengen visa application I have read several introductory texts about LSTM online, but none of them give a rigorously mathematical explanation of what the model actually does. For instance, why does the forget gate forget any more than any of the other gates in the LSTM unit?  Which papers and/or books should I read if I want to get a deeper understanding of LSTM? Switch command output language from native language to english On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) View revision history on mobile site It looks like it's currently not possible to view the revision history of a post from the mobile site. I think it would be a lot simpler than loading the desktop site on a phone just to get the revision history. Output of getent group No indentation after theorem environment with amsthm I use the amsthm package and dont want lines which start right after the theorem environment to be indented. I consulted the manual of the package and it said to define a new theorem style. I expected the following MWE to accomplish this task.  \documentclass[12pt,a4paper]{scrreprt}  \usepackage{amsthm} \newtheoremstyle{abcd}% name   {}%      Space above, empty = `usual value'   {}%      Space below   {\itshape}% Body font   {}%         Indent amount (empty = no indent, \parindent = para indent)   {\bfseries}% Thm head font   {.}%        Punctuation after thm head   {.5em}% Space after thm head: \newline = linebreak   {}%         Thm head spec \theoremstyle{abcd}  \newtheorem{defn}{Definition} \begin{document} \begin{defn} Some defintion \end{defn} This sentence shouldn't be indented. \end{document}   However, I end up with this   That is what I would expect (obtained using a noindent right after the theorem environment ends) How do you import CA certificates onto an Android phone? I want to connect to my University's wireless using my Nexus One. When I go to "Add Wi-Fi network" in Wireless Settings I fill in the Network SSID and select 802.1x Enterprise for the security and fill everything out.  The problem is that our university's wireless uses Thawte Premium Server CA certificate for certification.  When I click the drop down list for CA certificate I get nothing in the list (just N/A)  Now I have the certificate (Thawte Premium Server CA.pem) and have moved it to my SD card, but it doesn't look like Android automatically detects it.  Where should I put the certificate so that the Android wireless manager recognizes it. In other words, how can I import a CA certificate so that Android recognizes that it is on the phone and displays it in the CA Certificate drop down list.  Thanks for any help,  Tomek  P.S. My phone is not rooted  EDIT: After doing some research it looks like you are able to install certificates by going to your phone's settings > Location &amp; Security > Install from SD card  Unfortunately it looks like the only accepted file extension is .p12. It does not look like there is a way to import .cer or .pem files (which are the only two files that come with the Thawte certificates) at this moment.  It does look like you can use a converter to convert your .cer or .pem files to .p12, however a key file is needed.    I do not know where to get this key file for the Thawte certificates. Defining font color inside highlight fails Since I wanted a better readability of highlights of a would be black &amp; white-printed document, I needed to change both the highlighting color (gray) AND the font color (white).  Depending which command you implement inside the other will compile or not: \hl{\textcolor{white}{Fail}} does not work, compiling returns Package xcolor Error: Undefined color '{white}'.  Here's the mwe:  \documentclass{article} \usepackage{xcolor} \usepackage{color} \usepackage{soul} % Enables highlighting \sethlcolor{gray}  \begin{document}      \textcolor{white}{\hl{Success}}     %% Error:     %% Package xcolor Error: Undefined color `{white}'.     \hl{\textcolor{white}{Fail}}  \end{document}   So, in the end, the problem is sorta solved but I thought you might have an answer as to what happens. How do the Flashes breathe utilizing their super speed? The air pressure would be extreme. Do they run in a pressurized bubble?