I'm beginning to study logic and was reading Graham Priest's , and he includes this inference:      $q, \lnot q / p$.   He then provides a truth table. But, for the life of me, I can't figure out what he's doing (he doesn't state it, which makes me feel even dumber) The final configuration of Ts and Fs for the final 'p' is (from top to bottom) TFTF, with the initial truth-value reference table for q and p being (naturally):   q: TTFF p: TFTF  Whence does he derive that particular configuration for the final 'p'? Is it that because the premise states 'q' and then negates it, it says nothing and therefore the truth values for p stay the same? I know I could have asked this more clearly, but I'm a little desperate
I'm not sure how to prove these basic theorems in propositional calculus. Instead of using the standard axioms, we're supposed to use:   Deduction Theorem (if $\Phi, \alpha \vdash \beta$ then $\Phi \vdash \alpha \to \beta$),  Reductio (if $\Phi, \alpha \vdash \, $, then $\Phi \vdash \lnot \alpha$), Cut Rule (if $\Phi \vdash \alpha$ and $\Psi, \alpha \vdash \beta$ then $\Phi \cup \Psi \vdash \beta$),  Inconsistency Effect (if $\Phi \vdash \, $, then $\Phi \vdash \beta$ for every formula $\beta$), and  the Principle of Indirect Proof (if $\Phi, \lnot \alpha \vdash \, $, then $\Phi \vdash \alpha$),    as all the axioms can be deduced using these theorems.  I don't really know how to start the proofs without using the axioms:  i) prove that $\lnot(\alpha \to \beta) ⊢ \alpha$  ii) prove that $\lnot\alpha \vdash \alpha \to \beta$  Any suggestions on how to start these proofs or any insight at all would be greatly appreciated!  Thanks!
Xbox Game bar after uninstalling UWP and disabling UAC It looks like the  update  from Microsoft.  I have  and  UWPs as much as I can, along with Cortana and Edge.  Yet today I saw a weird green bar popup saying something about "Press Win + G to bring up the game bar".  I figured it would have to do with the Xbox UWP app, which I have previously uninstalled.  I presume this is UWP functionality, but I'm not sure how to find out for certain.  Can this app or program exist outside of the UWP ecosystem?  Is it a part of the Xbox app?  What method(s) are there to remove it?  Is there a prophylactic to prevent such things in the future?  I'm currently stuck in Windows Home, even though I  (not me, but gives you context).  I will be fixing that sometime soon. I used to use a lot ctrl+alt+numpad to move windows, how can I use this feature on ubuntu 18 like it was default before?  Thank you in advance Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$ Step to step how to install Cinelerra I have some problems installing cinelerra on my Ubuntu.  How do I install it? I have the following equation, where there is a lot of stuff under the sum symbol:  \begin{equation} d(\vec{x},\vec{y})=   \sum_{Z_{xy}\in\vec{Z}_{xy},\forall x\in\vec{x},\forall y\in\vec{y}}      f(Z_{xy}) \end{equation}   In the resulting document, I find it kind of hard to read. Is there a way to write the equation to make the result more readable, e.g. putting the stuff under the sum symbol on different lines? I am asking this question because I've always had the impression that manuscripts submitted to a journal in my field (theoretical linguistics) take an insanely long time to get published, and sometimes I get the impression that this is because, most of the time, nobody other than the author cares about getting things done within a reasonable amount of time. Some examples from personal experience follow.   For the last paper I submitted before getting my PhD, I had to wait nine months from the submission date to get reviews back from the referees. Last week I got a review request from a journal I had never reviewed for previously. The review deadline is March 15 (almost four months). In early October, I submitted a manuscript to a journal that I know asks reviewers to return reviews within 6 weeks. I checked the status of the manuscript online and it still says "with editor". Earlier this year, I was about to start writing a review when my wife went into labor. By the time we came back from the hospital, I had forgotten about the review, so I missed the deadline. The editor didn't contact me to ask about the review until two months after the deadline. Late in 2013, I was asked to write a survey chapter for a handbook. The expected publication date of the handbook is summer 2016.   All of this is not me being unlucky with editors and referees. In private conversations through the years, many colleagues have confirmed that it is virtually unheard of to get reviews back within 3 months of submission; 5 or 6 months seems to be a good average, but in some cases it can take longer (see my first point above). In general, everybody seems to have accepted that the submission-to-printed-journal process is going to take a bare minimum of one year, and that's assuming that the manuscript is accepted without revisions. If revisions are required, two years is not out of the question. Also, it's not like our papers are ridiculously long. I've reviewed about 100 papers so far, and the longest one was about 50 single-space pages; 30-35 single-spaced pages is closer to average.  I remember that, when I was a postdoc, my astrophysics housemate mentioned that in his field the entire submission-to-printed-journal process took only three or four months. I really can't see a good reason why theoretical linguistics shouldn't operate on similar timeframes, other than the fact that everybody seems to have grown used to things taking way longer than they really need to. What are the wait times in other fields? How do you manage to get things done quickly? How to find the most famous questions on Stack Overflow? How to find questions with   most comments most votes most viewed   I have seen following question, but seems like there is no easy way.   Is there way to bookmark a page so that the same URL can be used to update data (which will be very seldom) at each hit? Haproxy not logging captured request headers with custom log format Earlier i was not specifying a custom log format, and the captured request headers were getting printed fine. I wanted to log the unique-id-header, but could not find any way of doing so. So i copy pasted the log-format mentioned on , and unique id started getting logged.  Unfortunately, now the captured request headers are not getting logged. The %hrl and %hsl are coming out as empty strings.  Very weird. Here is my config, plzz help :(  listen server   bind *:80   mode http    option  httplog   option  http-server-close   no option logasap   # disable early logging of HTTP requests so that total transfer time is logged   option  forwardfor   capture request  header    X-Forwarded-For      len 500    capture request  header    Host                 len 500    capture request  header    X-Request-UID        len 500    rspadd  X-Haproxy-Backend:\ server    # Generate the X-Haproxy-Unique-ID and log it to make it easy to track requests   log-format %Ci:%Cp\ [id=%ID]\ [%t]\ %f\ %b/%s\ %Tq/%Tw/%Tc/%Tr/%Tt\ %st\ %B\ %cc\ %cs\ %tsc\ %ac/%fc/%bc/%sc/%rc\ %sq/%bq\ {%hrl}\ {%hsl}\ %{+Q}r   unique-id-format %{+X}o\ %Ci:%Cp_%Fi:%Fp_%Ts_%rt:%pid   unique-id-header X-Haproxy-Unique-ID   Here is the log i see:  Sep 13 17:28:57 localhost haproxy[11979]: 10.161.27.218:41592  [id=0AA11BDA:A278_0AA15B71:0050_505217C5_0014:2ECB] [13/Sep/2012:17:28:37.567]  server www-example-com-healthz/- 19998/0/2/1/+20001 200 +326  - - ---- 10/10/1/1/0 0/0 {} {}  "GET /testing/healthz?merchant=www.example.com&amp;source=elb HTTP/1.1"   Note that %hrl and %hsl are empty strings :( How do i capture the request headers ?? At the end of the game, both remaining players have a Baron.   The sum of all cards discarded by both players is equal.  Who wins? When is it a good idea to let an academic department (or a professor) know that I have Asperger's (or ADD)? With Asperger's, the trick is always when to explain it (in a non-awkward situation). I'd like to avoid mentioning it if possible, but it has gotten to the point that I only mention it after committing a major social faux pas, in which case it might be seen as an excuse.  With ADD, this is an issue that happens when people explain things to me. I often don't parse things very well when they're communicated to me verbally since I do have attention lapses. That's the major issue, anyways.   With that said, I do (indirectly) imply that I have both diagnoses on my personal website. Projection of a point onto a simple convex polytope I have a convex polytope described by the intersection of a hypercube and two parallel lower and upper hyperplanes cutting through the hypercube. I want to find the projection of a point onto the polytope. I read the question  and see that the general problem of finding a projection onto a convex polytope can be solved with quadratic programming. However, taken alone, projection onto a hypercube or a hyperplane is trivial. For the hypercube, each dimension is defined by a lower+upper bounds and we just pull each dimension within those bounds, which take $O(n)$ time in $n$ dimensions. For the hyperplane just find the projection onto it. So I'm wondering whether there is simpler method for finding such a projection, maybe somehow combining the two independent projections. How do I suppress stderr warning messages from a command inside command substitution? touch ~/deleted/$(echo "directory_"$(readlink -f foo)|tr '/' '\') 2&gt; /dev/null   where foo is a directory  It's reading the full pathname of foo and creating it as a file replacing all '/' with '\' and putting a directory_ in front so the directory  /home/test/foo would create a file directory_\home\test\foo  It does exactly what I want except a warning keeps printing tr: warning: an unescaped backslash at end of string is not portable   a. I don't know what that means b. I would like it to not show  I tried to redirect stderr to /dev/null but it doesn't work. How do I suppress it? Is there any way to block websites without Root access I am searching for a way to block websites without having root access. Is there any way to do it? Any help will be appreciated. How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity? Tensor product in dual-space I am a bid confused regarding the notation for tensor products when going into dual-space  If $\left| \Psi \rangle \right. = \left| A \rangle \right. \left| B \rangle \right.$ is $ \left. \langle \Psi \right| = \left. \langle A \right| \left. \langle B \right|$ or $\left. \langle B  \right| \left. \langle A \right|$?  My guess is the last choice, since operators should act on   $\left| 0 \rangle \right. = \left( \begin{matrix}   1 \\   0  \end{matrix} \right) $  $\left| 1 \rangle \right. = \left( \begin{matrix}   0 \\   1  \end{matrix} \right) $  so  $\left| 01 \rangle \right. = \left| 0 \rangle \right. \left| 1 \rangle \right. = \left( \begin{matrix}   0 \\   1 \\   0 \\   0  \end{matrix} \right) $  But then, for me, it should be  $\left( \begin{matrix}   0 &amp; 1 &amp; 0 &amp; 0  \end{matrix} \right) = \left \langle 10 \right|$ But this is not correct if i calculate the tensor product, since   $\left \langle 1 \right| \left \langle 0 \right| = \left( \begin{matrix}   0 &amp; 0 &amp; 1 &amp; 0  \end{matrix} \right)$  For instance, shoulden't it be  $\left| 01 \rangle \right. \left \langle 10 \right| = \left( \begin{matrix}   0 &amp; 0 &amp; 0 &amp; 0\\   0 &amp; 1 &amp; 0 &amp; 0\\   0 &amp; 0 &amp; 0 &amp; 0\\   0 &amp; 0 &amp; 0 &amp; 0\\  \end{matrix} \right) $ ?  I hope I have made my confusion clear How to make wget faster or multithreading? I've just upgraded my computer hardware(cpu + motherboard + graphic card + memory + hard disk), so that install a new OS is needed. I tried to download debian-6.0.6-amd64-netinst.iso with wget command but the speed is so slow that I could not bear. 4Kb/s ~ 17 Kb/s, slow like a running turtle, or even more slower if I use Chrome.  I've read the help information of wget, it seems like there are no options could make it more faster.  Is there anyway to make wget faster? Or is it possible to make it multi-threading download?  PS: my bandwidth is 4M. I use this command:  wget -c url  http://hammurabi.acc.umu.se/debian-cd/6.0.6/amd64/iso-cd/debian-6.0.6-amd64-netinst.iso Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective How can I proof this:     Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective, i.e., there are $A,B \in \mathbb{R}^2$ such that $A \neq B$ and $f(A) = f(B)$ (Hint: show that given $(a,b) \in \mathbb{R}^2$ in every open neighbourhood of $(a,b)$ there are points $(c,d),(c_1,d_1)$ where ${\partial}_1f(c,d) \neq 0$ or ${\partial}_1f(c_1,d_1) \neq 0$).   The problem is that I have no idea how to use the hint.  Thanks for all your comments. No space following macro without argument Can we set privacy for "last seen" status? I was wondering how to make a clickable terminal shortcut for my desktop using the command easytether connect.  I don't want to have to open/close the terminal every time I wish to connect to the Internet through my phone.  I've tried updating my gnome-panel but I can only make a new directory on my desktop.