Is a vacuously true argument a valid argument?
Could an argument with false Premises and a true Conclusion be logically valid?
How does Meta Stack Exchange work? Meta Stack Exchange seems to have different rules and user behavior than the "regular" Stack Exchange sites.  How is it different?    Individual questions answered below:                Related Direct Link to a Comment The increase in the character limit of comments has led them to become as important as the questions and answers that spawn them. On several occasions (especially on meta) I've found reason to want to link to a comment directly. I'd imagine something as simple as making the date / time stamp an anchored link which mimics the behavior of the question link. When lasers are used to cool atoms or ions, etc where does the heat go? According to the first law of thermodynamics, sourced from wikipedia "In any process in an isolated system, the total energy remains the same."  So when lasers are used for cooling in traps, similar to the description here:  where is the heat transferred?    From what I gather of a cursory reading on traps, whether laser, magnetic, etc the general idea is to isolate the target, then transfer heat from it, thereby cooling it.  I don't understand how sending photons at a(n) atom(s) can cause that structure to shed energy, and this mechanism seems to be the key to these systems. Fantasy series with Celtic overtones, intermittent stone magic, and ongoing slow magic I checked this series out of the library during college, maybe 15 years ago now.    It was based around 'stone magic' – magical stones that granted their bearers enormous power.  Unfortunately, the power of these stones is intermittent, they'll fade out for a long time then fade back in.  The main characters dealt with a 'master' stone of some sort, the first to restore, last to die.  It's also the key to granting other people access to their own powers – I think seals had magic fish they swallowed, which keyed off the master stone, and in the last book I think the character created magic staves for another race. It also had 'slow magic' – longer to set up, less apparently potent than stone magic, but the slow magic, given time to work it, could still be powerful and dramatic.  It just took time and preparation instead of brute force. In one book, the main character faces off against the source (or something like that) of magic, and is about to win when it's discovered she's pregnant.  The source – a dragon? – isn't allowed to harm anyone who doesn't come to it freely, so the main character is forbidden to finish the trial.  In the sequel, her daughter repeats the trial, and becomes immensely powerful by winning, but there was a cost of some sort, something that transformed her A lot of the naming made me think it had a Celtic root. Calculation of the avalanche effect coefficient Given a  matrix/dependence matrix for a hash function,how do I calculate the avalanche coefficient for it. I want to calculate a single parameter(value) which represents the amount of avalanche effect for the given hash function.  I have thought of computing mean all over the matrix but am not sure that's the correct thing to do.  The  talks about the avalanche coefficient but they haven't mentioned the way they calculate it. C++ cout hex values? The cardinality of $\{f\subseteq\mathbb R^2\mid f\colon\mathbb{R\to R}\text{ is a function}\}$ is strictly greater than the cardinality of $\mathbb R$ Isometries of the sphere $\mathbb{S}^{n}$ Java obfuscators I'm looking for a good Java obfuscator.  I've done initial research into the following Java obfuscators: proguard, yguard, retroguard, dasho, allatori, jshrink, smokescreen, jobfuscate, marvin, jbco, jode, javaguard, jarg, joga, cafebabe, donquixote, mwobfu, bbmug, zelix klassmaster, sandmark, jcloak, thicket, blufuscator, and java code protector.  I tried proguard and it has a really nice GUI, seems really stable, and seems to be the most popular, but it seemed to not like some enumeration on a referenced jar file (not within the code I was trying to obfuscate) which was weird.  Yguard seems to require some interaction with ant, which I didn't know too much about.  What is a good java obfuscator?  It doesn't need to be free, it just needs to work well and be easy to use. How to capture the scene exactly as my eyes can see? Proof of dividing fractional expressions For dividing two fractional expressions, how does the division sign turns into multiplication? Is there a step by step proof which proves  $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}=\frac{ad}{bc}?$$ Connecting Asus USB-N13 Wireless Adapter I'm trying to connect my desktop (running 64-bit Ubuntu 12.04) to an Airport Extreme Base Station by using an ASUS USB-N13 wireless adapter.  I plugged it in, turned on the desktop, and the adapter was immediately recognized by the system. I found my home network listed in the available networks, typed my password (with the correct encryption) and hit connect. After that, the wireless icon just flashes (propagates? emits?) indefinitely, and every couple of minutes the "Wireless Authentication Required" box pops back up.   I don't know what to do. I've seen some solutions talking about an "rt2xxx" or "rt3xxx" driver or chipset. I don't know exactly what it is, but when I typed lsmod | grep rt I got:  parport_pc rtl8192cu rtl8192c_common rtlwifi mac80211 cfg80211 parport   I'm pretty much lost. Please AskUbuntu, what do? How do we use drupal_add_library(), drupal_add_css() and drupal_add_js()? How do I use drupal_add_library(), drupal_add_css() and drupal_add_js() in Drupal 8?  I am porting a module that uses those functions. I am following what reported in , which says these functions have been removed in favor of #attached, but I am not able to attach these files to my configuration page.  The error I am getting is the following:     Uncaught PHP Exception LogicException: "You are not allowed to use js in #attached"   How do I attach CSS and JavaScript to a page? Gravitational waves as dark energy? Programmatically combining images in PHP I'm a big fan of Yahoo's  for speeding up websites. One of the recommendations is to combine images where possible to cut down on size and the number of requests. However, I've noticed that while it can be easy to use CSS sprites for layouts, other image uses aren't as easily combined. The primary example I'm thinking of is a blog or article list, where each blog or article also has an image associated with it. Those images can greatly affect load time and page size, especially if they aren't optimized. What I'm looking for, in concept or in practice, is a way to dynamically combine those images while running them through a loss-less compression using PHP.   A few added thoughts or concerns:   Combining the images and generating a dynamic CSS stylesheet to position the backgrounds of the images might be one way to go about it, but I also worry about accessibility and semantics. As far as I understand, CSS images should be used for layout elements and the img tag (with the alt attribute) should be used for images that are meant to convey information. I could set the image as a background to a div element and substitute a title attribute for the alt attribute, but I'm unsure about the accessibility and semantic implications of doing so. Might the GD library be a good candidate for something like this? Can you recommend other options? I've been having a lot of problems trying to figure out how to use scanf().  It seems to work fine with integers, being fairly straight forward scanf("%d", &amp;i).  Where I am running into issues is using scanf() in loops trying to read input.  For example:  do {   printf("counter: %d: ", counter);   scanf("%c %c%d", &amp;command, &amp;prefix, &amp;input); } while (command != 'q');    When I enter in a validly structured input like c P101, it seems to loop again before prompting me.  This seems to happen even with a single:  scanf("%c", &amp;c)    in a while loop.  It'll do the loop twice before prompting me again.  What is making it loop twice, and how do I stop it? When I enter in less amount of input that programmatically wouldn't have another character or number such as q, pressing enter seems to prompt me to enter more.  How do I get scanf() to process both single and double character entries? Flight reservation for Schengen visa One of the necessary documents for a Schengen visa for non EU citizens is proof of your flights, but it doesn't state the actual (e-)tickets (for which I already paid), or the reservation of flights.  So my question is, which option would be more acceptable (if I can provide any of them) to provide printed tickets to an EU member embassy or reservation of flights (reservation does not expect payment)? Balloons and lifting gases Hydrogen is the lightest element, so it's cable of lifting the most weight in out atmosphere (probably not the best terminology there, but you get the picture)  Would hot hydrogen (in the same sense as hot air) be able to lift even more mass? Would a higher or lower density of hydrogen in a ballon lift more? If you could have a balloon which had nothing in it (it was a vacuum inside) would that lift more than a hydrogen balloon?  Basically what are the physics to balloons and lifting?  (really not sure what to tag this, so if someone else could that'd be great) I need to conduct a performance test on Azure website and the Users count is '200000'. Can anyone suggest me the configuration for this? Possible Duplicate:          I was wondering if there's any good reason to still use blob fields in a database. A couple of years ago I worked with a DB with a bunch of images in it, the DB was very slow and I couldn't see any good reason to keep the images inside the DB, so I got the images out and stored the filenames instead.  Was this a smart move? What would you do in my place?