How do we know that the number $1$ is not equal to the number $-1$?
Proof that in a field $x=0$ is equivalent to $x=-x$
Is it possible to produce such design hints (on elements padding, spacing, width, height) automatically in photoshop? Is there any plugin that can potentially do this? USB WiFi dongle device that can emulate a virtual mass storage device for a home video player Is there a USB WiFi dongle device that can:   Emulate a virtual mass storage device for a home video player But in fact shows the files from a network-shared folder? What are words like "Hey Man", "Hey you", "Hey Dude" called Is there a term for words that summon someone like "Man," "Dude," "Kid" in sentences such as "Hey, Dude," "Listen up, kid," etc?    I am sure there is, but I can't really remember what it is. Why do two bodies of different masses fall at the same rate (in the absence of air resistance)? What is the mass density distribution of an electron? Protect Google Spreadsheet formatting while allowing changes to data I would like to protect the formatting of a cell (or a range of cells) in a Google Spreadsheet, but still allow changing the data in that (or those) cell(s).  For example, I want to add a validation rule on a cell that says the cell has to contain a number between 1 and 10, and I would like others to be able to change the value in that cell, but not the validation rule itself.  How do I do that?  So far I was only able to completely protect the cell (content + formatting) or not at all (the user can change the content as well as the formatting).  To me this seems to be an important functionality when adding access rights to spreadsheets. Is it possible that it is completely missing from Google Spreadsheets? Is there a more accurate way to create a Javascript timer than setTimeout? Something that has always bugged me is how unpredictable the setTimeout() method in Javascript is.  In my experience, the timer is horribly inaccurate in a lot of situations. By inaccurate, I mean the actual delay time seems to vary by 250-500ms more or less. Although this isn't a huge amount of time, when using it to hide/show UI elements the time can be visibly noticeable.  Are there any tricks that can be done to ensure that setTimeout() performs accurately (without resorting to an external API) or is this a lost cause? Why are certain example URLs like https://site.com/ and https://mysite.com/ blocked from post content? Does a constantly accelerating charged particle emit EM radiation or not? How do I recruit beta testers? We're a small company without enough employees to run a large scale beta in house.  The app is geo-location based so we're trying to recruits some beta testers from all over that aren't "friends and family".  Are there any sites or communities dedicated to something like this? Finding the volume of the tetrahedron. Find the volume of the tetrahedron with the vertices $P(1,1,1)$, $Q(1, 2, 3)$, $R(3, 1, 2)$, and $S(2, 3, 1)$. My computer wont shutdown If I try to shutdown my computer it simply takes me back to the login-screen. I looked around and found :  Type in terminal:   sudo gedit /etc/default/grub Find the line: GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" Change this to:GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi=force" Save the file and close the file.  Finally, in terminal: sudo update-grub   But now there is a new problem when I try step 5 it says:  *myname*@ubuntu:~$ sudo update-grub [sudo] password for *myname*:  /usr/sbin/grub-probe: error: cannot find a device for / (is /dev mounted?). *myname*@ubuntu:~$    I am new whit linux and dont know what to do. Getting polygon shapefile node coordinates and point order I can think of three general ways of explaining why the universe contains more matter than antimatter:  (1) Near the Planck time, the universe had zero baryon asymmetry, but at some later time, determined by some GUT energy scale, the  were satisfied, and the baryon asymmetry became nonzero.  (2) Nonconservation of baryon number occurs only at Planckian energies. Near the Planck time, the baryon asymmetry evolved from zero to some nonzero value.  (3) The Sakharov conditions have never been satisfied. The baryon asymmetry has always been nonzero, and has simply scaled as expected. (Apparently one  $\Delta n=n_B-n_\bar{B}\propto s$, where $n$ is number density and $s$ is entropy density).  It seems like most theorists are interested in #1, but is there any reason why 2 and 3 aren't possible?  2 seems pretty reasonable, since for the reasons given in , we have good reasons to think that baryon number is not conserved under Planckian conditions.  3 also seems reasonable to me, since even if baryon number is nonconserved at Planckian energies, that's only one of the three Sakharov conditions. I don't see any obvious fine-tuning objections to #3, since the scaling of baryon asymmetry with cosmological expansion isn't particularly drastic (not an exponential decay or anything). Is there something unphysical about maintaining $\Delta n\propto s$ all the way back to the Planckian era?   Some people might object to #3 on aesthetic grounds, since we "expect" the initial conditions of the universe to be symmetric, but that seems weak to me. After all, we don't object aesthetically to the fact that homogeneity was an imperfect symmetry of the early universe, and we even accept that the early universe was in a thermodynamically unlikely state. My initial problem was that my computer wouldn't let me login to my account. It seems to shut down after I enter my password. I can login as a guest.  I found fixes but I can't remember / figure out my login for access after I hit Ctrl+Alt+F1 and most of the fixes for finding your login username depend on you having access to your account.  I thought the login was the name which appears on the screen when I start the computer normally, but this has not worked, is there another way to find out my username while being effectively locked out of my root-user profile?  I am also assuming that the password is the same one I always use.  Conversely, if the name which appears on the screen at startup and my normal password should have worked, is there another explanation for why I am not able to login on the black command screen. Solving ODE with negative expansion power series I am solving a series of ODE, such that each DE is equal to some degree of term that I'm expanding to. For instance, one DE is this:  $\xi^r\partial_r g_{rr}+2g_{tt}\partial_t\xi^t=\mathcal{O}(r)$  $g_{ii}$ are given, from metric, but that's not important. I need to assume that the solution (since I'm looking for components of $\xi^\mu$, which is a vector with components $\xi^t,\xi^r,\xi^\phi$) is given with power series of the form:  $\xi^\mu=\sum\limits_{n}\xi^\mu_n(t,\phi)r^n$, and this is to be seen as expansion around $1/r$ (expansion around $r=\infty$).  Now when I plug this in the ODE I get this  $\frac{2}{l^2}\sum_n\xi^r_nr^{n+1}+2\sum_n\xi^t_{n,t} r^n+\frac{2}{l^2}\sum_n\xi^t_{n,t}r^{n+2}=\mathcal{O}(r)$, where   $\xi^\mu_{n,i}$   is the derivative with the respect to i-th component.   What troubles me is, how to expand this? Do I set n=0,-1,-2,... until my $\mathcal{O}(r)$ terms cancel each other out? Or?  I'm kinda stuck :\ I've been playing Agar for some time now, and lately I've noticed there was a new XP system in Agar. Since then I've been wondering what variables chance the XP gained. I've tried googling it, but with no luck.  I'm looking for how the XP system works in these game modes:   FFA Teams Experimental Is it possible to enable System Protection from the command prompt? delayed addclass/remove class function not working PDF export on macOS Mojave produces bold fonts