When we push a box, the box applies an opposite force on my hand, but why does my hand move with the box as I push the box if the net force of is 0?
When we push a box, the box applies an opposite force on my hand, but why does my hand move with the box as I push the box if the net force of my hand is 0? What is happening?
How can I see all versions of a package that are available in the archive? Is there a way I can see all the versions that are in the archives that I have configured in sources.list. I can see the last version of each archive withapt-get policy, but how can I see them all?  Is there any way that this can also include PPA and anything in sources.list.d? Let $f,g:X\to Y$ be maps of spaces such that $f\simeq g$. Is it true that the mapping cones $\operatorname{cone}(f)$ and $\operatorname{cone}(g)$ are homotopy equivalent?  Can we write down an explicit homotopy equivalence? It ought not to be too hard to get a map $\operatorname{cone}(f)\to \operatorname{cone}(g)$ from the existence of a homotopy $H:X\times I\to Y$, but I haven't been able to find a sensible candidate, despite trying for quite a while. At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon? Six simple tips to get Stack Overflow reputation fast From "6 Simple Tips to Get Stackoverflow Reputation Fast" at codexon.com:   Be the First to Answer. Even at the cost of quality. Use Downvotes and Comments Strategically Use obnoxious in-your-face formatting and lists. Be Aware of the 200 rep/day Limit Edit, But Don’t Edit Too Much Associate your other accounts   Courtesy of . Agree? Disagree? Walnuts? Cantaloupe? "No such file or directory" when trying to remove a file, but the file exists? I am trying to remove a png image that was uploaded to my server via a PHP script. Whenever I try to delete it both through ftp and terminal, I get the error   No such file or directory   However, when I ls in the dir, the file is listed and it is also listed in my ftp client. I have tried creating a file with the same name and I end up getting two files with the same name.   I can open the file that supposedly does not exist, but I still can't remove it. I have also tried rebooting my server. Any ideas what may be the issue? I am running a 64 bit version of Ubuntu, but I don't think its a 32/64 bit issue. I should also note I have removed many other png files uploaded by the same PHP script.  Output for ls -l  total 224  -rw-r--r-- 1 www-data www-data 222838 May 13 04:14 qyxdshyikfr_fishing_timeout.png  -rw-r--r-- 1 root root 272 May 14 06:54 upload.php   Output when trying to rm  rm: cannot remove ‘qyxdshyikfr_fishing_timeout.png’: No such file or directory   upload.php: How to make the measuring grid larger? When starting the blender, there is always a cube on the floor. The floor is actually a grid. My question is how to make this grid bigger so that we can measure big stuff? If you are talking on behalf of you and someone else what is the correct usage?  On behalf of my wife and me On behalf of my wife and I On behalf of me and my wife On behalf of myself and my wife On behalf of my wife and myself ...  My understanding is that after that phrase you would carry on talking in first person. "Now" vs "by now" Consider these examples:   By now the desk should be looking significantly tidier!  By now, the failure of regulators to contain dangerous forces should be well accepted.  By now I own some forty copies of the magazine.  By now the blue of twilight is glowing.  He used leverage, but by now applied concerted discipline to contain his risks.    I wonder if I can use &quot;now&quot; instead of &quot;by now&quot; to convey the same meaning. I would think &quot;by now&quot; refers to a moment until now, but why not use past tense or present perfect tense in the these examples? How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure? I (think) that I've configured a static IP address in /etc/network/interfaces:  # The primary network interface  auto eth0  iface eth0 inet static     address 10.1.1.2     netmask 255.255.255.0     network 10.1.1.0     broadcast 10.1.1.255     gateway 10.1.1.1   And I change the file /etc/resolv.conf to include the desired nameservers.   Then I restart networking sudo /etc/init.d/networking restart  But after some hours resolv.conf always reverts back to the DHCP nameserver.   I should also say that this is Ubuntu Server with only l0 and eth0 interfaces. I'm just starting to learn LaTeX. I tried typing \begin{equation*}  (math goes here)  \end{equation*}  and I got a whole bunch of errors. It seems LaTeX interpreted the empty line as the equation: when it saw nothing there, I guess it just ended math mode? It then said my other commands needed $'s so I assume that's what happened. When I typed \begin{equation*} (math goes here) \end{equation*}  everything was fine. So I'm confused. If LaTeX sees an empty line in an environment, does it just interpret this as me changing my mind, and deciding not to use the declared environment? Mysql crashed, dumped DB's in recovery mode. What now? Recommendations on a free library to be used for zipping files I need to zip and password-protect a file. Is there a good (free) library for this?  This needs to be opened by a third party, so the password protection needs to work with standard tools. I recently got the book "selected problems in real analysis", and I'm stuck solving the very first problem  $(u_n)$ is a binary sequence iff it only contains $0$ and $1$ in the sequence  Let $A$ be the set of all binary sequences  I have to prove that $A$ and ${2}^{\mathbb{N}}$ have the same cardinality, that is to say there exists a 1-1 function from one set to another  I've thought about maybe considering integers as base-2 numbers  Thanks for your help $\sqrt{1-x^2}$ is not a rational function If $k$ is a field in which $1 + 1 \neq 0$, prove that $\sqrt{1-x^2}$ is not a rational function. Hint. Mimic the classical proof that $\sqrt{2}$ is irrational   It seems rather odd to discuss the square root function in the context of an arbitrary field, but here goes nothing!  Proof:   Suppose that $\sqrt{1-x^2}$ is a rational function in $k(x)$. Then there exist polynomials $p(x)$ and $q(x) \neq 0$ that are relatively prime with $\sqrt{1-x^2} = \frac{p(x)}{q(x)}$; clearly we may take $p(x) \neq 0$. Then $1-x^2 = \frac{p(x)^2}{q(x)^2}$ or $q(x)^2(1-x^2) = p(x)^2$, which says $q^2 | p^2$, and since $q | q^2$, we can infer $q | p^2$. Moreover, since $p|p^2$ and $(p,q)=1$, then $pq|p^2$ or $q|p$, which contradicts the fact that the polynomials are relatively prime. Hence $\sqrt{1-x^2}$ cannot be a rational function.    How does this sound? Aside from the problem of discussing $\sqrt{~~}$ in the context of an arbitrary field, I am worried about not using the fact that $1+1 \neq 0$, at least not explicitly. Where exactly is this assumed used, if at all?  EDIT:  Suppose that $q(x) =1$, and let $f(x) = a_n x^n + ... a_1 x + a_0$. Then $1-x^2 = f(x)^2$. If $x=0$, $1 = a^2_0$ and therefore $a_0$ must be a unit. Letting $x=1$ we get $0 = (a_n + ... + a_1 + a_0)^2$; and letting $x=-1$ we get $0 = (-a_n - ... - a_1  + a_0)^2$. Since we are working in a field, there can be no nonzero nilpotent which means that $a_n + ... + a_1 + a_0$ and $-a_n - ... - a_1  + a_0$ are both zero. Adding the two equations together yields $2a_0 = 0$, and since $1+1 \neq 0$, $a_0 = 0$ which contradicts the fact that $a_0$ is a unit.   How does this sound?  Another attemtpt:  If $f(x)^2 = 1-x^2$, then $2 = \deg(f^2) = 2 \deg (f)$ implies $\deg(f) = 1$. Yet if $x=-1$, we get $f(-1)^2 = 1 - 1 = 0$ and therefore $f(-1)=0$ since there are no nonzero nilpotent elements in a field; similarly, $f(1)=0$. Since $1+1 \neq 0$, $f$ has two distinct roots in $k$ yet is only a $1$-st degree polynomial, a contradiction. Proof that a sequence is convergent On Chrome on Android, code blocks on the mobile site have no syntax highlighting, are not a monospaced font, and words are wrapped.  Mobile site on mobile browser:    Desktop site on mobile browser:    Inline code has the same issue, it isn't a monospaced font.  It has been this way for as long as I can remember. Wouldn't be surprised if this is a dupe. Convergence of $\sqrt{n}x_{n}$ where $x_{n+1} = \sin(x_{n})$ Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$ Let $x$ and $y$ be integers not congruent to $0$ modulo $p$ where $p$ is a prime. Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$.   I thought about proving this algebraically and by contradiction. So we say $x^2+y^2 = pz$ and have to show this is impossible. Two Clash of Clans accounts on one device I have been playing on two clash of clans accounts on one device for a long time but just recently i cannot switch from my lvl17 to my lvl75. The switch villages option is not popping up for me and I don't know why. Can anyone help me get my main account back?