Prove the following theorem:  ⊢ (P → Q) → (¬ Q → ¬ P) Prove the following equivalence:  (P ∧ Q) → R    ⊣ ⊢     P → (Q → R) Prove the following set of sentences inconsistent: {P → (Q → R), ¬ R ∧ (P ∧ Q)
I can't seem to figure out how to get past this step. Any suggestions?
Product of Consecutive Integers is Not a Power There was the following paragraph in the article that came under the title, “GOP and the rise of Anti-knowledge” written by  (October 29, 2015):     “English unfortunately doesn’t have a precise word for the German   “Fachidiot,” a narrowly specialized person accomplished in his own   field but a blithering idiot outside it. In any case, a surgeon is   basically a skilled auto mechanic who is not bothered by the sight of   blood and palpitating organs. We need the surgeon’s skills on pain of   agonizing death, and reward him commensurately but that does not make   him a Voltaire.”    In Japanese we have a word, 専門バカ, of which literal translation is “specialist idiot” meaning exactly same as defined the above - a narrowly specialized person accomplished in his own field but a blithering idiot outside it.  I’m really curious about the absence of short descriptions of the specialist who knows nothing more than his specialty area in English like German “Fachidiot,” and Japanese "専門バカ."  Isn’t there really any short word counterpart to “Fachidiot,” specialist’s ignorance, for instance, in English?  P.S.  I found "narrow-minded specialisit" as a German-to-English translation of "fachidiot" in the web site, Interglot translation dictionary. Automate fixes for issues found by Sonar So here is what i want to pull : mmcblk0 whith it's size 15.7 GB.  C:\adb&gt;adb shell shell@android:/ $ su su shell@android:/ # fdisk -l /dev/block/mmcblk0 fdisk -l /dev/block/mmcblk0  Disk /dev/block/mmcblk0: 15.7 GB, 15758000128 bytes 1 heads, 16 sectors/track, 1923584 cylinders Units = cylinders of 16 * 512 = 8192 bytes   This is what I tried:  C:\adb&gt;adb shell su busybox cat /dev/block/mmcblk0 &gt; C:\1.bin   I only have 1KB output with content inside said "unknown id". Also tried with pull but seems also doesn't work.  What should I do to get this 15.7 GB mmcblk0  ? SQL Server 2008 server cannot connect to itself with alias name or "localhost" We have a SQL Server 2008 ENT 64bit SP3 server running Server 2008 R2 Standard SP1 64-bit.  This is also a windows/sql clustered environment.  There is the cluster alias for the server, and then we have 2 AD DNS aliases as well for the server  Suddenly I can't connect to the sql instance in Management Studio, or with a Powershell Invoke-SQLcmd IF I am doing it from that actual server, when using one of the dns alias names, or "localhost".  If I use the Cluster alias name it works and if I use the other dns alias name it works.  Using management studio with the non-working dns alias I get "Login failed. The login is from an untrusted domain and cannot be used with Windows authentication."  If I use localhost, I get "A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 2)"    Shared Memory and TCPIP are enabled in SQL Server Config manager but named pipes is not.  But we've NEVER had named pipes enabled, and don't have it enabled on any of our other sql servers and they're set up the same (clustering, dns aliases...etc) and are having no issues.  I've Googled around and had a view people suggest listing what other SQL servers it can see (cmd prompt sqlcmd -L)  If it do it from a good server I see all other servers on my network including the "bad" one.  If I do that command from the "bad" server, I get no results at all.  Pretty much checked everything from this blog and it's all ok except the sqlcmd -L issue I just mentioned above.    Windows firewall is not enabled.  This was working just fine for a couple of years.  I'm not sure when this started happening, but I know that at some point, it was not happening.  And the other kicker...it's only happening locally to this server.  If I connect with management studio or run a powershell Invoke-Sqlcmd from another machine, or my local machine connecting to the "bad" server, it works fine no matter what alias I use.  I'm stumped.  I think it sounds like an issue with the AD alias (there are 2 ad aliases, 1 works locally the other doesn't)...but not being able to connect with localhost makes me question that.  any help is greatly appreciated. How to install Intel CedarView drivers on Ubuntu 12.10 or higher? I am looking for instructions on how to install cedarview graphics drivers on Ubuntu 13.04 32bit.  My graphics hardware is a GMA3600 aka Power VR SGX545.  EDIT: It seems that they are not in Raring yet, but only Precise:   EDIT2: they seem to be closed source. How can continue the equation of the rectangle red in next line?   \documentclass[11pt,a4paper,twocolumn]{article}  ...  \begin{equation*}     \left| \dot{r} \right| =     \sqrt{{- \, {e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {{e}^{-t} \left( \cos t + \sin t \right)}^{2} \, + \, {(- \, {e}^{-t})}^{2}} \end{equation*} Setting up SFTP to log in to server with Filezilla I have an ec2 instance on AWS which already installed a few Wordpress-es in it.  I want to set things up to let more people handle their own projects, with me also being able to go into the server using terminal if I still want to.  I have been following tutorials such as  and a few others.  I figured all of them just teach users how to sftp into their own home folder, also the steps keep saying addUser but some users already existed and removing them might cause some issue.  How can I give existing users the permission to use SFTP for Wordpress projects?  Let's say all my Wordpress projects are already under /var/www/ which has already been set up with www-data:www-data.  Really new with setting things like this.  Thanks in advance for any help. In the NEW CANON why don't the Rebels abandon Yavin 4 before the Death Star Arrives? nginx open reverse proxy? Somehow, and I'm not sure how, we have configured an nginx reverse proxy that is acting as an open proxy.  The log files tells us the matching requests are going against the following conf file:  map $http_upgrade $connection_upgrade {         default upgrade;         ''      close; }  access_log      /var/log/nginx/access.p.log; error_log       /var/log/nginx/error.p.log;  proxy_next_upstream     error timeout invalid_header http_500 http_502 http_503 http_504; proxy_buffers           8 32k; proxy_buffer_size       64k; proxy_http_version      1.1; proxy_set_header        Host            $host; proxy_set_header        X-Real-IP       $remote_addr; proxy_set_header        X-Forwarded-For $proxy_add_x_forwarded_for; proxy_redirect          off; proxy_set_header        Upgrade         $http_upgrade; proxy_set_header        Connection      $connection_upgrade;  server {         listen          80;         server_name     ~first.*\.second\.com;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              http://$host;                 proxy_read_timeout      7200s;         } }  server {         listen          443;         server_name     ~first.*\.second\.com;         ssl             on;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              https://$host;                 proxy_read_timeout      7200s;         } }   The top-level conf file looks like this:  user nginx; worker_processes 8; pid /var/run/nginx.pid;  events {         worker_connections 4096;         # multi_accept on; }  http {      ##     # Basic Settings     ##      sendfile on;     tcp_nopush on;     tcp_nodelay on;     keepalive_timeout 65;     types_hash_max_size 2048;     # server_tokens off;      # server_names_hash_bucket_size 64;     # server_name_in_redirect off;      include /etc/nginx/mime.types;     default_type application/octet-stream;      ##     # Logging Settings     ##      access_log /var/log/nginx/access.log;     error_log /var/log/nginx/error.log;      ##     # Gzip Settings     ##      gzip on;     gzip_disable "msie6";      # gzip_vary on;     # gzip_proxied any;     # gzip_comp_level 6;     # gzip_buffers 16 8k;     # gzip_http_version 1.1;     # gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss text/javascript;      ##     # nginx-naxsi config     ##     # Uncomment it if you installed nginx-naxsi     ##      #include /etc/nginx/naxsi_core.rules;      ##     # nginx-passenger config     ##     # Uncomment it if you installed nginx-passenger     ##      #passenger_root /usr;     #passenger_ruby /usr/bin/ruby;      ##      include /etc/nginx/conf.d/*.conf;     #include /etc/nginx/sites-enabled/*;   }  what here is causing this? How to disable Macbook Pro internal display when using external monitors I have a Late 2011 Macbook Pro 13" (running Lion - OS 10.7.4) which I use with a dual external monitor setup. I have two 21" LCDs that I use as external monitors. One uses the built in Mini Display Port on the Macbook Pro and the other is connected via a USB to DVI adapter (Diamond DVILink).  The problem I am having is with the 13" built in display of the Macbook Pro. I would like it to remain closed and unused (I prefer the dual monitors at same resolution), however I cannot seem to "disable" the display in the display preferences applet. So even though the Macbook Pro lid is closed the operating system still makes use of the display, even though the apple logo on the back of the display is unlit. I have tried to move the laptop screen off out of the way in display preferences but I find when I "sleep" my setup that any applications that remain open move to the laptop screen. This makes it difficult to locate the application windows when resuming from sleep.    Does anyone know of a way to disable the laptop built in display so it is not seen by the OS when external monitors are being used? Defining my own None-like Python constant Setup or "set up"? The word setup (as a noun), I feel, has become an acceptable part of the English language, at least insofar as technical manuals or computer textbooks are concerned. However I find that the word is used very often in verb form like so:     "You can setup the program quite easily ..."   when in fact my understanding is that the actual sentence should be:     "You can set up the program quite easily ..."   I would like to know if setup can be used as a verb. The situation seems be very similar to the word output (as a noun). Output is a purely technical word and its use is restricted solely to technical texts or at least in a technical context within non-technical books. However it is also used in verb form now like so:     "The system will output the signal ..."   I would be very grateful if this question is answered. Thank you I am new to Stack  Exchange and I think it's very impressive.  One thing bothers me is that because it is so far down the line, I don't think beginners stand a chance of growing.  As time goes on, more and more questions are being answered and therefore if someone asks something with a really basic answer you can just comment. However, beginners can't comment until they have a reputation of 50. The only way they can build up is by answering questions. But if they answer a basic question long winded, they will be voted down because not so much effort was needed or because its already a duplicate and will lose the bit of reputation they have earned.  Can you tell me the future for beginners? Why does the buffer take up whole screen? I am trying to create buffers around the Hurricane Sandy path I created in QGIS (points are lat/long).   I have both points from each day she was tracted and the line I created from it with Points2One.   When I go to make buffers around either the line or the points, the buffer takes up the whole screen. Its all just one color.   I have made buffers before but from data I did not create.   Right now all of my projections are set to WGS 84 EPSG 4326. Penalized models can be used to estimate models where the number of parameters is equal to or even greater than the sample size. This situation can arise in log-linear models of large sparse tables of categorical or count data. In these settings, it is often also desirable or helpful to collapse tables by combining levels of a factor where those levels are not distinguishable in terms of how they interact with other factors. Two questions:   Is there a way to use penalized models such as LASSO or elastic net to test for the collapsibility of levels within each factor? If the answer to the first question is yes, can, and should, this be set up in such a way that the collapse of levels and the estimation of model coefficients occurs in a single step? If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$ I am working on some past prelim problems and one of them is the following: If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$   Update: Following Jackie Chong's advice, I am attempting this problem with the dominated convergence theorem. Since $f\in L^1(\mathbb{R})$, $f$ can be approximated from below by a sequence of continuous functions $f_n$. Then, I believe I can say that, for all $n$ sufficiently large, $|f_n(x+\frac{1}{n})-f_n(x)|\le 2|f(x)|$. (I'm not sure of this part thought). Then $2|f(x)|$ is integrable and hence a dominating function for $|f_n(x+\frac{1}{n})-f_n(x)|$. So by the dominated convergence theorem we can take the limit inside $\lim_{n\rightarrow \infty}\int|f_n(x+\frac{1}{n})-f(x)|dx=\int \lim_{n\rightarrow \infty}|f_n(x+\frac{1}{n})-f(x)|dx=0$ Is this on the right track?  Another approach that I thought may work, but which I'm less certain of is the following: If $f$ can be approximated by $C^1$ functions (I have no real justification for this, so please correct me if its wrong), then for each $n$ and each $x$ there is some $y(x,n)\in B_{1/n}(x)$ such that $|f(x+\frac{1}{n}-f(x)|=\frac{1}{n}|f'(y(x,n)|$ but from here I don't see how to proceed, because just because $|f|$ is integrable, I can't justify $|f'|$ being integrable, but if there is some way to fix this approach, hints would be appreciated.   Another thing I was thinking was to first approximate $f$ from below by continuous functions $f_n$ then to define $g_{m,n}=|f_n(x+\frac{1}{m})-f_n(x)| \chi_{[-m,m]}$. Then, for each $n$, the function $g_{m,n}$ is continuous on its support, and since it support is compact, it is uniformly continuous there. Can this be used to justify bringing the limit $\lim_{n\rightarrow \infty}$ inside the integral? Then apply the monotone convergence theorem? I know this idea is probably even more sketchy than my previous one, but if it can be fixed please let me know :)  Thanks! Is there a math basis for what I observe in simulations? MAC addresses in JavaScript I know that we can get the MAC address of a user via IE (ActiveX objects).  Is there a way to obtain a user's MAC address using JavaScript? Anyone ever seen a "wok adapter" for induction cooktops? In theory a cheap pressed steel wok would work on an , but the "contact patch" for a traditional round bottomed wok would be so small it would be ineffective.  Has anyone seen a steel or cast-iron "wok adapter" with a flat bottom and a concave "bowl" on top to sit the wok in, serving dual purposes of supporting the wok on the stovetop and transferring the induction heat to the wok?  Could anyone speculate if this would this even work? Or wouldn't you be able to get the wok hot enough?