How to make a smaller gap when using many level of $$$$?
How to split a very long equation (using AMSMATH package)?
Multiple monitors, multiple workspaces? I connected my laptop to my LCD. Using the laptop display hotkey I can switch between different modes - only laptop monitor on, only LCD monitor on, both on and display the same view, both on and the desktop is stretched (divided).  But, I'm looking for something else - I would like to have two workspaces, one visible on the laptop monitor and the other on the LCD.  Is that possible? I do not have much experience in table design. My goal is to create one or more product tables that meet the requirements below:   Support many kinds of products (TV, Phone, PC, ...). Each kind of product has a different set of parameters, like:   Phone will have Color, Size, Weight, OS... PC will have CPU, HDD, RAM...  The set of parameters must be dynamic. You can add or edit any parameter you like.   How can I meet these requirements without a separate table for each kind of product? Can you intentionally fail a skill check? This comes up to me in the context of the 3.x/PF/d20 Fly skill, even when I simply read about it: Can you intentionally fail a Fly skill check, or any other skill check for that matter, if you, or your character for that matter, decides that the effects of failing the check are what is desired in the situation?  Example:  Take a a shapeshifted Draconian cruising at high altitude, with a few friends on his back who have some means of breathing air supply, whether it be mundane or magical.  Now lets say that the air supply goes kablooie, similar to a decompression or all-packs-trip in an airliner.  For the sake of the folks on his back -- if not himself, depending on if dragon forms need supplemental air to fly at such high altitudes, the Draconian has to lose altitude, and fast.  Considering that by RAW, a Fly check failure leaves yourself falling, would saying "I initiate a rapid descent" be enough to treat the next Fly check as an intentional failure, or would you have to roll a 'reverse' Fly check, where failing the check gives you the desired outcome of a rapid descent, and succeeding leaves you stuck at altitude?  P.S. I added the rules-as-written tag because a RAW answer is highly desired here, albeit not mandatory.  I can already mostly figure it out from a simulationist standpoint, but that answer involves going in-depth into airline flying and non-normal procedures. Fetching all (javascript) global variables in a page Format string dynamically I know you can select a tag and then click on unanswered to view the unanswered questions for that tag.  But is there a way to view questions only for a certain set of tags > 1 tag?  Mainly I'd like the union of tag1 with tag2 with tag3 with tag4. But also the intersection of tags would be nice as well. Cards changing mana color What cards across all sets allow the utilization of mana, either colorless or otherwise, as colored mana of another color?  One early example with an unlimited  1:1 ratio:     Sunglasses of Urza   Continuous Artifact: White mana in your mana pool can also be used as red mana.   What other cards have similar abilities? Graphics crop in guest welcome window I don't expect that any user should have noticed this, since only guests will see them.  Well, it seems that the Stack Overflow welcome splash, containing the basic info of the site, is cropped from the bottom.    Please don't mind the sides, I cropped them to fit on the screen. Just on the bottom is my concern. Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$ This is a homework question whereby I am supposed to evaluate:  $$\sum_{n=1}^\infty \frac{1}{n^2 +1}$$  Wolfram Alpha outputs the answer as   $$\frac{1}{2}(\pi \coth(\pi) - 1)$$  But I have no idea how to get there. Tried partial fractions (by splitting into imaginary components), tried comparing with the Basel problem (turns out there's little similarities), nothing worked. Ctrl+Alt+← can usually be set to restart X, however I can't find the option to allow this (it is disabled by default).  I have looked in System-&gt;Preferences-&gt;Keyboard and System-&gt;Preferences-&gt;Keyboard Shortcuts but I can't find an option to enable it.  Where can I change this setting? Why does the command shuf file > file leave an empty file, but similar commands do not? I know this is sort of a duplicate of another question () but I wanted to expand on the question in response to the answers given.  The command  shuf example.txt &gt; example.txt  Returns a blank file, because the shell truncates the file before shuffling it, leaving only a blank file to shuffle. However,  cat example.txt | shuf &gt; example.txt  will produce a shuffled file as expected.  Why does the pipeline method work when the simple redirection doesn't? If the file is truncated before the commands are run, shouldn't the second method also leave an empty file? How many ways are there to select a pair of cards from a standard deck of cards such that one of the cards is red and the other one is black? Suppose that a pair of cards are selected from a standard deck of 52 cards. And since there are 26 black cards and 26 red cards, so I'm wondering if my thinking is right?   ${26!/25! * 26!/25!}$ so it would be ${26*26 = 676}$ Java GUI repaint() problem? I have a JFrame. This JFrame contains a JButton. I click the JButton and 10 JTextFields are created.  the problem: I cannot see them until "I force a repaint()" by resizing the window. Only then do I see the JTextFields created.  CODE:  JPanel points = new JPanel();  //Creating the JTextFields: for (int i=0; i&lt;10; i++) {     JTextField textField = new JTextField();     points.add(textField); }  repaint(); this.repaint(); super.repaint(); points.repaint();     THANK YOU - after the for loop, I just called points.validate() and it worked... Proof of an elementary property of Projection Operators I'm asked to show the following:  Let $X$ be a linear space, and let $P : X \rightarrow X$ be a projection operator. Restricted to the linear space $range(P)$, the projection $P$ is the identity operator, that is, $Px = x$ for all $x \in range(P)$.  If anyone could offer a hint for how to show this. I'm rusty with linear algebra so don't really know what I'm supposed to bring in outside of what's specified in the lemma/definition of projection. What is so special about the range of P that would make this so? What is the purpose of wrapping whole Javascript files in anonymous functions like “(function(){ … })()”? What information does the trace of a matrix give? Why is "high" pronounced "hiy" but is not spelled that way? How can I set default value in ActiveRecord?  I see a post from Pratik that describes an ugly, complicated chunk of code:   class Item &lt; ActiveRecord::Base     def initialize_with_defaults(attrs = nil, &amp;block)     initialize_without_defaults(attrs) do       setter = lambda { |key, value| self.send("#{key.to_s}=", value) unless         !attrs.nil? &amp;&amp; attrs.keys.map(&amp;:to_s).include?(key.to_s) }       setter.call('scheduler_type', 'hotseat')       yield self if block_given?     end   end   alias_method_chain :initialize, :defaults end   I have seen the following examples googling around:    def initialize      super     self.status = ACTIVE unless self.status   end   and    def after_initialize      return unless new_record?     self.status = ACTIVE   end   I've also seen people put it in their migration, but I'd rather see it defined in the model code.  Is there a canonical way to set default value for fields in ActiveRecord model? Segmentation Fault when attempting to print value in C Who in the DC Universe can stop Superman if he has a breakdown? Is there anything or anyone in the DC universe that can defeat Superman just in case he goes berserk on everybody?  Maybe Batman stores kryptonite in his Cave or something. I don't know if Batman actually has kyptonite, the example was just a theoretical example.  Who can stop Superman if needed, and how?