How can I prove $B ∨ ¬B$ without using assumption and contradiction?
Proving 'Law of Excluded Middle' in Fitch system
Does it have or has? Some packages, have a Provides: header. For example, the package postfix on Debian Wheezy has Provides: mail-transport-agent.   The package mail-transport-agent which doesn't exist physically is considered as a "virtual" package.   How can I know, on a Debian based system, if a given virtual package is "installed" (or "provided")? Can I list every "provided" virtual package?  Hint: to list every existing virtual package, installed or not, do: aptitude search "~v" How to conduct an Accent Sensitive search in MySql I have a MySQL table with utf8 general ci collation. In the table, I can see two entries:  abad abád  I am using a query that looks like this:  SELECT *  FROM `words` WHERE `word` = 'abád'   The query result gives both words:  abad abád  Is there a way to indicate that I only want MySQL to find the accented word? I want the query to only return    abád    I have also tried this query:  SELECT *  FROM `words` WHERE BINARY `word` = 'abád'   It gives me no results. Thank you for the help. How to effectively close a page? MWE for externalize + automatic recompilation after tikz figure modification How do I mount .vhd file? I'm using 13.04 Raring amd64 and I need to mount a .vhd file on my ubuntu. I've googled about it and found that virtualbox-fuse package is the answer.  But the package was deleted from apt repository. Is there any way to install the package w/ 13.04? or is there any alternative to virtualbox-fuse? Stop all active ajax requests in jQuery How to change color of the text in TextView on hover like in css? How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime Does mass distribution/center of mass affect free fall? An everyday is example would be cars. If you were to drop a car, not taking air resistance into account, would a front-heavy car tumble forward as it fell? And a car with a perfect 50/50 front/rear weight distribution fall straight? Does mass distribution/center of mass affect free fall? Or would they both fall straight down without tumbling? Can you explain why please? When I open a window to air out the room, how does the smell disperse? Let's say I'm in a room with some kind of noxious stink, possibly of flatulent nature.  The quickest way to right the world that comes to mind is to open a window.  When I open a window, how do the stank particles leave the room? Is it correct to say "I kindly request you to..."? Isn't kindness already implied when you say "I request you to..."?  When I say "I humbly request you to...", the word humbly helps me to label the state of my behavior during the request.  On the other hand, what value does the word kindly add to the request? Why KL divergence is non-negative? Why is KL divergence non-negative?  From the perspective of information theory, I have such an intuitive understanding:  Say there are two ensembles $A$ and $B$ which are composed of the same set of elements labeled by $x$. $p(x)$ and $q(x)$ are different probability distributions over ensemble $A$ and $B$ respectively.   From the perspective of information theory, $\log_{2}(P(x))$ is the least amount of bits that required for recording an element $x$ for ensemble $A$. So that the expectation $$\sum_{x \in  ensemble}-p(x)\ln(p(x))$$ can be interpreted as at least how many bits that we need for recording an element in $A$ on average.   Since this formula puts a lower bound on the bits that we need on average, so that for a different ensemble $B$ which brings about a different probability distribution $q(x)$, the bound that it gives for each element $x$ will surely not bit that is given by $p(x)$, which means taking the expectation, $$\sum_{x\in ensemble}-p(x)\ln(q(x))$$ this average length will surely be greater than the former one, which leads to $$\sum_{x\in ensemble }p(x)\frac{\ln(p(x))}{\ln(q(x))} &gt; 0$$  I don't put $\ge$ here since $p(x)$ and $q(x)$ are different.  This is my intuitive understanding, is there a purely mathematical way of proving KL divergence is non-negative? The problem can be stated as:  Given $p(x)$ and $q(x)$ are both positive over real line, and $\int_{-\infty}^{+\infty}p(x)dx = 1$, $\int_{-\infty}^{+\infty}q(x)dx = 1$.  Prove $$\int_{-\infty}^{+\infty}p(x)\ln\frac{p(x)}{q(x)}$$ is non-negative.  How can this be proved? Or can this be proved without extra conditions? Let $f:\mathbb{R}\to\mathbb{R}$ continuous such that $\lim_{x\to\infty}f(x+1)-f(x)=l$.  How can I prove that $\dfrac{f(x)}x$ converges for $x\to+\infty$ ?  I am just trying to prove the convergence, not that it converges to $l$ (that part be deduced immediately by Stolz-Cesaro and the sequential characterization of limits) Installing Autodesk Maya on Ubuntu is possible, but can be a bit challenging.  Assuming that one already has the required specs and a solid graphics card driver installed, how can it be done? How does ADR (Automated Dialogue Replacement) work?  There's an entry in Wikipedia that says what it is (essentially actors dubbing their lines in post production, sometimes requiring several takes) but I don't see what's "automatic" about it.  It doesn't seem to work all that well because I can almost always tell when it has been used. Converting time field omitting time and returning null values? I have a time field in my shapefile that is formatted as HH:mm:ss.s It is a text field, and I want to convert it to a date so I can calculate time elapsed across rows (if there's a better way to do this let me know). Basically, each row is a point on a route, and I want to use the time field to calculate the amount of time elapsed between the first and last points on the route.   I tried using the convert time field tool, setting the input format as HH:mm:ss.s, and the output type as DATE. The output field however only shows values of 01/01/2001 for some rows and  for other rows.   time is the input field and time_c is the output field  I'm not sure what's going wrong here, here is what shows up in the geoprocessing results window:    I tried adding the date data to the field as well to make the format yyyy-MM-dd HH:mm:ss.s, but it still didn't work: Any way to see mail sent by other user through shared address? My wife and I have a "shared" email address, like thesmiths@example.com which we both use from Gmail when we both want to get replies or for signing up for certain websites.  When an email is received at that address, it gets forwarded to both of our personal Gmail accounts.  The problem is that when either one of us "sends as" that address, the other does not see the sent message. So we have to cc or bcc each other (and she usually forgets.)  Is there any automagic way to have those sent emails appear in BOTH of our Gmail accounts?  I've tried filters but I don't think they work on outgoing messages. Basically we want a filter that would automatically forward emails from that address to the other person.  I know this can be done with standalone mail clients, but neither of us uses those. How to tail multiple files using tail -0f in Linux/AIX I tried tailing two files using the option:  tail -0f file1.log -0f file2.log   In Linux I see an error "tail : can process only one file at a time".  In AIX I see the error as "Invalid options".  This works fine when I use:  tail -f file1 -f file 2   in Linux but not in AIX.  I want to be able to tail multiple files using -0f or -f in AIX/Linux  multitail is not recognized in either of these OS. How to switch between virtual console and GUI in Ubuntu? I wanted to see what key functions would allow me to switch between the two.