Java doesn't know how to multiply? What?
Floating point arithmetic not producing exact results
Why is it safe to use 15 A receptacles on a 20 A circuit? Using induction, how can I show the following identity about the fibonacci numbers? I'm having trouble with simplification when doing the induction step.  Identity: $$f_n^2 + f_{n+1}^2 = f_{2n+1}$$  I get to:  $$f_{n+1}^2 + f_{n+2}^2$$  Should I replace $f_{n+2}$ using the recursion? When I do that, I end up with the product of terms, and that just doesn't seem right. Any guidance on how to get manipulate during the induction step?  Thanks! Why does a 'sudo -i' login shell break a here-doc command string argument? In the sequence of five commands below, all depend on single-quotes to hand off possible variable substitution to the called bash shell rather than the calling shell. The calling user is xx, but the called shell will be run as user yy. The first command substitutes $HOME with the calling shell's value because the called shell is not a login shell. The second command substitutes the value of $HOME loaded by a login shell, so it is the value belonging to user yy. The third command does not rely on a $HOME value and creates a file in the guessed home directory of user yy.  Why does the fourth command fail? The intention is that it writes the same file, but relying on the $HOME variable belonging to user yy to ensure it actually does end up in her home directory. I don't understand why a login shell breaks the behaviour of a here-doc command passed in as a static single-quoted string. The failure of the fifth command verifies that this problem is not about variable substitution.  xx@host ~ $ sudo -u yy bash -c 'echo HOME=$HOME' HOME=/home/xx xx@host ~ $ sudo -iu yy bash -c 'echo HOME=$HOME' HOME=/home/yy xx@host ~ $ sudo -u yy bash -c 'cat &gt; /home/yy/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' xx@host ~ $ sudo -iu yy bash -c 'cat &gt; $HOME/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' bash: warning: here-document at line 0 delimited by end-of-file (wanted `EOFscript-contentEOF') xx@host ~ $ sudo -iu yy bash -c 'cat &gt; /home/yy/test.sh &lt;&lt; "EOF" &gt; script-content &gt; EOF &gt; ' bash: warning: here-document at line 0 delimited by end-of-file (wanted `EOFscript-contentEOF')   These commands were issued on a Linux Mint 18.3 Cinnamon 64-bit system, which is based on Ubuntu 16.04 (Xenial Xerus).  Update: The here-doc aspect is just clouding the issue. Here's a simplification of the problem:  $ sudo bash -c 'echo 1 &gt; echo 2' 1 2 $ sudo -i bash -c 'echo 1 &gt; echo 2' 1echo 2   Why does the first of those two commands preserve the linebreak and the second does not? sudo is common to both commands, yet seems to be escaping/filtering/interpolating differently depending on nothing but the "-i" option. When I press F3 to see the debug screen in I use Minecraft 1.8.1, some information is missing.   Most notably, there are no X, Y, Z coordinates.     What happened to my debug overlay? Can FFMPEG extract images from a video with timestamps? Does the ANSI standard mandate the logical operators to be short-circuited, in either C or C++?  I'm confused for I recall the K&amp;R book saying your code shouldn't depend on these operations being short circuited, for they may not. Could someone please point out where in the standard it's said logic ops are always short-circuited? I'm mostly interested on C++, an answer also for C would be great.  I also remember reading (can't remember where) that evaluation order isn't strictly defined, so your code shouldn't depend or assume functions within an expression would be executed in a specific order: by the end of a statement all referenced functions will have been called, but the compiler has freedom in selecting the most efficient order.  Does the standard indicate the evaluation order of this expression?  if( functionA() &amp;&amp; functionB() &amp;&amp; functionC() ) cout&lt;&lt;"Hello world"; I am trying to remove the Facebook and Messenger apps from my Asus Zenphone Laser 2.  Unfortunately, in both cases, I seem to be unable to find the option to fully delete them from the device. I have disabled them, but the app management screen now shows the following:     How can I fully delete/uninstall them? TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen? Basic Electronics Book I have been reading Hamilton Chapter 13 and he has the following state space representation for an ARMA(p,q). Let $r = \max(p,q+1)$.Then the ARMA (p,q) process is as follows: $$ \begin{aligned}  y_t -\mu &amp;= \phi_1(y_{t-1} -\mu) + \phi_2(y_{t-2} -\mu) + ... + \phi_3(y_{t-3} -\mu) \\ &amp;+ \epsilon_t + \theta_1\epsilon_{t-1} + ... + \theta_{r-1}\epsilon_{t-r+1}.  \end{aligned} $$ Then, he defines the State Equation as follows:   $$  \xi_{t+1} = \begin{bmatrix}      \phi_1 &amp; \phi_2 &amp; \dots &amp; \phi_{r-1} &amp; \phi_r \\      1 &amp; 0  &amp; \dots &amp; 0 &amp; 0  \\      \vdots &amp; \vdots &amp; \dots &amp; 0 &amp; 0 \\      0 &amp; 0 &amp; \dots &amp;1 &amp;0 \end{bmatrix} \xi_t  +  \begin{bmatrix}      \epsilon_{t+1} \\     0\\\vdots  \\     0       \end{bmatrix}  $$  and the observation equation as:  $$y_t = \mu + \begin{bmatrix}      1 &amp; \theta_1 &amp; \theta_2 &amp; \dots &amp; \theta_{r-1} \\     \end{bmatrix} \xi_t. $$  I do not understand what the $\xi_t$ is in this case. Because in his AR(p) representation it is $\begin{bmatrix}      y_{t} - \mu \\     y_{t-1} - \mu\\\vdots  \\     y_{t-p+1} - \mu       \end{bmatrix}  $ and in his MA (1) representation it is $\begin{bmatrix}      \epsilon_{t} \\     \epsilon_{t-1}      \end{bmatrix}  $.  Could someone explain this to me a little bit better? Is $v=\ (r_i)^{-1}\cdot z $, a uniformly random value of a field? We consider a finite field $\mathbb{F}_q$ where $q=2p+1$ and $q$ and $p$ are prime numbers.  Let $r_i$ be a value picked uniformly at random from the field such that $r_i&gt;\frac{q}{2}$. Let $z$ be a fixed field element.   Question: Is $v=(\ (r_i)^{-1}\cdot z) \bmod q$, a uniformly random value of the field? During real, everyday use, that is?  I'm looking to upgrade a drive in a MacBook Pro, and am looking at either a 750GB/7200RPM or a 1TH/5400RPM drive.  Would I care about the speed difference? Is it worth giving up the additional space on the larger drive? How to change from csh to bash as default shell I have csh as my default shell, as shown by echo $SHELL. I want to switch to bash as my default shell. I tried the following approaches to no avail:   With chsh I get:  chsh: can only change local entries; use ypchsh instead.  With ypchsh I get:  ypchsh: yppasswdd not running on NIS master host ("dcsun2").    I only have .chsrc in my home directory and I cannot find any .profile files in /etc. How can I change my default shell to bash? How to prove polynomials with degree $n$ does not form a vector space? This is one of my linear algebra problems:     Prove that polynomials of degree $n$ does not (The professor made these words bold intentionally) form a vector space.   From what I read, the set of polynomials of degree $n$ should be a vector space, because:   There is an "One" and a "Zero" in this set; We can find inverse for addition and multiplication from this set; It follows all the axioms of addition. It follows all the axioms of scalar multiplication.   Then can someone give me some hints to prove it does not form a vector space? Halo particles don't render in Cycles I want my app automatically know user phone number by accessing their SIM Card Are "w/o", "w/", "b/c" common abbreviations in the US? Name of a special matrix I have a matrix which is kind of symmetrical with the other diagonal, i.e., something like  $$A = \left[ \begin{array}{c c c c}    a &amp; b &amp; c &amp; d \\    e &amp; f &amp; g &amp; c \\    h &amp; i &amp; f &amp; b \\    j &amp; h &amp; e &amp; a  \end{array} \right]$$  Does this matrix have a special name in literature? What are it's properties?  And a matrix that is symmetrical by both diagonals   $$A = \left[ \begin{array}{c c c c}    a &amp; b &amp; c &amp; d \\    b &amp; e &amp; f &amp; c \\    c &amp; f &amp; e &amp; b \\    d &amp; c &amp; b &amp; a  \end{array} \right]$$  What's the name of it? Any interesting properties? What does ':' (colon) do in JavaScript? What is a good SSH server to use on Windows? In my spare time I remotely support my wife's office via VPN into a Windows Server. I am about to purchase a wireless broadband service which doesn't support VPN.  I don't want to open up the remote desktop ports directly, and I would like to set up an SSH tunnel into the network, and if necessary then VPN over the top of that.  What is the best windows SSH Server implementation to use on a Windows 2003 Server, or should I just be using ?